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Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.1) The table below shows the number of new AIDS cases in the U.S. in each of the years 1989-1994.

Year New AIDS cases1989 33,6431990 41,7611991 43,7711992 45,9611993 103,4631994 61,301

Classify the study as either descriptive or inferential.A) Descriptive B) Inferential

1)

2) Based on a random sample of 1000 people, a researcher obtained the following estimates of thepercentage of people lacking health insurance in one U.S. city.

Age Percentage not covered18-24 28.225-39 24.940-54 19.155-65 16.5

Classify the study as either descriptive or inferential.A) Descriptive B) Inferential

2)

3) A researcher randomly selects a sample of 100 students from the students enrolled at a particularcollege. She asks each student his age and calculates the mean age of the 100 students. It is21.3 years. Based on this sample, she then estimates the mean age of all students enrolled at thecollege to be 21.3 years. In what way are descriptive statistics involved in this example? In whatway are inferential statistics involved?

A) When calculating the mean age of the students in the sample, the researcher is usinginferential statistics. When estimating the mean age of all students at the college, theresearcher is using descriptive statistics.

B) When calculating the mean age of the students in the sample, the researcher is usingdescriptive statistics. When estimating the mean age of all students at the college, theresearcher is using inferential statistics.

3)

1

4) A news article appearing in a national paper stated that ʺThe fatality rate from use of firearms sankto a record low last year, the government estimated Friday. But the overall number of violentfatalities increased slightly, leading the government to urge an increase in police forces in majorurban areas. Overall, 15,600 people died from violent crimes in 2005, up from 15,562 in 2004,according to projections from a government source. Is the figure15,600 a descriptive statistic or aninferential statistic? Is the figure 15,562 a descriptive statistic or an inferential statistic?

A) The figure15,600 is a descriptive statistic since it reflects the actual number of deaths fromviolent crimes for the year 2004. The figure15,562 is an inferential statistic since it is indicatedin the statement that it is a projection (probably based on incomplete data for the year 2005).

B) The figure15,600 is an inferential statistic since it is indicated in the statement that it is aprojection (probably based on incomplete data for the year 2004). The figure15,562 is aninferential statistic as well.

C) The figure15,600 is a descriptive statistic since it reflects the actual number of deaths fromviolent crimes for the year 2005. The figure15,562 is a descriptive statistic as well.

D) The figure15,600 is an inferential statistic since it is indicated in the statement that it is aprojection (probably based on incomplete data for the year 2005). The figure 15,562 is adescriptive statistic since it reflects the actual number of deaths from violent crimes for theyear 2004.

4)

Answer the question.5) 100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day

and only 45% said yes. Identify the sample and population.A) Sample: the 100,000 selected adults; population: the 45% of adults who drink at least 48 oz of

waterB) Sample: the 45% of adults who drink at least 48 oz of water; population: all adultsC) Sample: the 100,000 selected adults; population: all adultsD) Sample: all adults ; population: the 100,000 selected adults

5)

Identify the study as an observational study or a designed experiment.6) 400 patients suffering from chronic back pain were randomly assigned to one of two groups. Over

a four-month period, the first group received acupuncture treatments and the second groupreceived a placebo. Patients who received acupuncture treatments improved more than those whoreceived the placebo.

A) Designed experiment B) Observational study

6)

7) An examination of the medical records of 10, 000 women showed that those who were short andfair skinned had a higher risk of osteoperosis.

A) Designed experiment B) Observational study

7)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.8) Why do statisticians sometimes use inferential statistics to draw conclusions about a

population? In what situations might a statistician draw conclusions about a populationusing descriptive statistics only?

8)

2

9) At one hospital in 1992, 674 women were diagnosed with breast cancer. Five years later,88% of the Caucasian women and 63% of the African American women were still alive.This observational study shows an association between race and breast cancersurvival--that Caucasian women are more likely to survive breast cancer than AfricanAmerican women. How could this study be modified to make it a designed experiment?Comment on the feasibility of the designed experiment that you described.

9)


List all possible samples from the specified population.10) Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the

possible samples (without replacement) of size four that can be obtained from the group.A) A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E B,C,E,A B,D,E,A

C,A,B,D C,E,D,B D,A,C,EB) A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,EC) A,B,C,DD) A,B,C,D A,B,C,E A,C,D,E A,D,E,B

10)

Provide an appropriate response.11) The finalists in an essay competition are Lisa (L), Melina (M), Ben (B), Danny (D), Eric (E), and

Joan (J). Consider these finalists to be a population of interest. The possible samples (withoutreplacement) of size two that can be obtained from this population of six finalists are as follows.

L,M L,B L,D L,E L,J M,B M,DM,E M,J B,D B,E B,J D,E D,J E,J

If a simple random sampling method is used to obtain a sample of two of the finalists, what are thechances of selecting Lisa and Danny?

A) 215

B) 16

C) 13

D) 115

11)

12) From a group of 496 students, every 49th student starting with the 3rd student is selected. Identifythe type of sampling used in this example.

A) Simple random sampling B) Cluster samplingC) Systematic random sampling D) Stratified sampling

12)

13) An education researcher randomly selects 38 schools from one school district and interviews all theteachers at each of the 38 schools. Identify the type of sampling used in this example.

A) Stratified sampling B) Cluster samplingC) Simple random sampling D) Systematic random sampling

13)

14) At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A schooladministrator selects a simple random sample of 12 of the freshmen, a simple random sample of 9of the sophomores, a simple random sample of 11 of the juniors, and a simple random sample of 8of the seniors. She then interviews all the students selected. Identify the type of sampling used inthis example.

A) Cluster sampling B) Systematic random samplingC) Simple random sampling D) Stratified sampling

14)

3

15) A pollster uses a computer to generate 500 random numbers and then interviews the voterscorresponding to those numbers. Identify the type of sampling used in this example.

A) Stratified sampling B) Systematic random samplingC) Cluster sampling D) Simple random sampling

15)

A designed experiment is described. Identify the specified element of the experiment.16) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to

one of three groups. Over a one-month period, the first group received a low dosage of anexperimental drug, the second group received a high dosage of the drug, and the third groupreceived a placebo. The diastolic blood pressure of each participant was measured at the beginningand at the end of the period and the change in blood pressure was recorded. Identify theexperimental units (subjects).

A) The participants in the experimentB) The three different groupsC) The treatment (i.e., placebo, low dosage of drug, or high dosage of drug)D) The diastolic blood pressures of the participants

16)

17) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned toone of three groups. Over a one-month period, the first group received a low dosage of anexperimental drug, the second group received a high dosage of the drug, and the third groupreceived a placebo. The diastolic blood pressure of each participant was measured at the beginningand at the end of the period and the change in blood pressure was recorded. Identify the responsevariable.

A) The treatment received (placebo, low dosage, high dosage)B) The dosage of the drugC) Change in diastolic blood pressureD) The participants in the experiment

17)

18) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned toone of three groups. Over a one-month period, the first group received a low dosage of anexperimental drug, the second group received a high dosage of the drug, and the third groupreceived a placebo. The diastolic blood pressure of each participant was measured at the beginningand at the end of the period and the change in blood pressure was recorded. Identify the factor.

A) Diastolic blood pressure B) The experimental drugC) The participants in the experiment D) The dosage of the drug

18)

19) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned toone of three groups. Over a one-month period, the first group received a low dosage of anexperimental drug, the second group received a high dosage of the drug, and the third groupreceived a placebo. The diastolic blood pressure of each participant was measured at the beginningand at the end of the period and the change in blood pressure was recorded. Identify the levels ofthe factor.

A) Diastolic blood pressure at the start, diastolic blood pressure at the endB) Placebo, low dosage, high dosageC) High blood pressure, low blood pressureD) The experimental drug

19)

4

20) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned toone of three groups. Over a one-month period, the first group received a low dosage of anexperimental drug, the second group received a high dosage of the experimental drug, and thethird group received a placebo. The diastolic blood pressure of each participant was measured atthe beginning and at the end of the period and the change in blood pressure was recorded.Identify the treatments.

A) Placebo, low dosage of drug, high dosage of drugB) Low dosage of drug, high dosage of drugC) Diastolic blood pressure at start, diastolic blood pressure at endD) The experimental drug

20)

21) A herpetologist performed a study on the effects of the body type and mating call of the malebullfrog as signals of quality to mates. Four life-sized dummies of male bullfrogs and two soundrecordings provided a tool for testing female response to the unfamiliar frogs whose bodies variedby size (large or small) and color (dark or light) and whose mating calls varied by pitch (high,normal, or low). The female bullfrogs were observed to see whether they approached each of thefour life-sized dummies. Identify the treatments.

A) The eight different possible combinations of the two body sizes, two body colors, and twomating call pitches

B) The twelve different possible combinations of the three body sizes, two body colors, and twomating call pitches

C) The eighteen different possible combinations of the two body sizes, three body colors, andthree mating call pitches

D) The twelve different possible combinations of the two body sizes, two body colors, and threemating call pitches

21)


Provide an appropriate response.22) Explain the difference between an observational study and a designed experiment. 22)

23) In a designed experiment, explain the difference between the treatments and the factors. 23)

24) A study was conducted to evaluate the effectiveness of a new diet pill for men. A group of3000 men were involved in the study. Of these 3000 men, 2311 took the diet pill and 889were given a placebo. Identify the treatments, the treatment group, and the control group.

24)


Classify the data as either qualitative or quantitative.25) The following table gives the top five movies at the box office this week.

Rank Last week Movie title Studio Box office sales ($ millions)1 N/A Pirate Adventure Movie Giant 35.22 2 Secret Agent Files G.M.G. 19.53 1 Epic Super Hero Team 21st Century 14.34 5 Reptile Ride Movie Giant 10.15 4 Must Love Cats Dreamboat 9.9

What kind of data is provided by the information in the second column?A) Qualitative B) Quantitative

25)

5

26) The following table gives the top five movies at the box office this week.

Rank Last week Movie title Studio Box office sales ($ millions)1 N/A Pirate Adventure Movie Giant 35.22 2 Secret Agent Files G.M.G. 19.53 1 Epic Super Hero Team 21st Century 14.34 5 Reptile Ride Movie Giant 10.15 4 Must Love Cats Dreamboat 9.9

What kind of data is provided by the information in the third column?A) Qualitative B) Quantitative

26)

Classify the data as either discrete or continuous.27) The number of freshmen entering college in a certain year is 621.

A) Discrete B) Continuous27)

28) The average height of all freshmen entering college in a certain year is 68.4 inches.A) Discrete B) Continuous

28)

Identify the variable.29) The following table shows the average weight of offensive linemen for each given football team.

Team Average weight (pounds)Gators 303.52Lakers 326.78Eagles 290.61Pioneers 321.96Lions 297.35Mustangs 302.49Rams 345.88Buffalos 329.24

Identify the variable under consideration in the second column?A) pounds B) GatorsC) team name D) average weight of offensive linemen

29)

Tell whether the statement is true or false.30) A discrete variable always yields numerical values.

A) True B) False30)

31) The possible values of a discrete variable always form a finite set.A) True B) False

31)

32) A variable whose values are observed by counting something must be a discrete variable.A) True B) False

32)

33) The set of possible values that a variable can take constitutes the data.A) True B) False

33)

6

34) A discrete variable can only yield whole-number values.A) True B) False

34)

35) A variable whose possible values are 1.15, 1.20, 1.25, 1.30, 1.35, 1.40, 1.45, 1.50, 1.55, 1.60, is acontinuous variable.

A) True B) False

35)

36) A variable which can take any real-number value in the interval [ 0, 1 ] is a continuous variable.A) True B) False

36)

37) A personʹs blood type can be classified as A, B, AB, or O. In this example, ʺblood typeʺ is thevariable while A, B, AB, O constitute the data.

A) True B) False

37)

38) Arranging the age of students in a class in from youngest to oldest yields ordinal data.A) True B) False

38)


Construct a grouped-data table for the given data. Use the symbol to mean ʺup to, but not includingʺ.39) A medical research team studied the ages of patients who had strokes caused by stress.

The ages of 34 patients who suffered stress strokes were as follows.

29 30 36 41 45 50 57 61 28 50 36 5860 38 36 47 40 32 58 46 61 40 55 3261 56 45 46 62 36 38 40 50 27

Construct a frequency table for these ages. Use 8 classes beginning with a lower class limitof 25.

Age Frequency

39)

7

40) A government researcher was interested in the starting salaries of humanities graduates. Arandom sample of 30 humanities graduates yielded the following annual salaries. Data arein thousands of dollars, rounded to the nearest hundred dollars.

23.1 24.0 33.7 28.4 36.0 41.0 22.2 21.8 30.5 49.2 30.1 25.2 38.3 46.1 40.0 27.5 24.9 28.0 31.8 29.9 25.7 32.5 48.6 27.4 41.4 35.9 31.9 42.4 26.3 33.0

Construct a grouped-data table for these annual starting salaries. Use 20 as the firstcutpoint and classes of equal width 4.

Salary Frequency

40)

Construct a grouped-data table for the given data. Use the alternate method for depicting classes. Using this method, therange of values that go into a given class includes both cutpoints. So the class 30 -39, for example, would contain valuesfrom 30 up to and including 39.

41) A medical research team studied the ages of patients who had strokes caused by stress.The ages of 34 patients who suffered stress strokes were as follows.

29 30 36 41 45 50 57 61 28 50 36 5860 38 36 47 40 32 58 46 61 40 55 3261 56 45 46 62 36 38 40 50 27

Construct a frequency table for these ages. Use 8 classes beginning with a lower class limitof 25.

Age Frequency

41)

8


Construct a frequency distribution for the given qualitative data.42) The blood types for 40 people who agreed to participate in a medical study were as follows.

O A A O O AB O B A O A O A B O O O AB A A A B O A A O O B O O O A O O A B O O A AB

Construct a frequency distribution for the data.A) Blood type Frequency

O 19A 13B 5AB 3

B) Blood type FrequencyO 19A 11B 5AB 2

C) Blood type FrequencyO 18A 14B 5AB 3

D) Blood type FrequencyO 20A 13B 4AB 3

42)

Provide the requested table entry.43) The data in the following table show the results of a survey of college students asking which

vacation destination they would choose given the eight choices shown. Determine the value thatshould be entered in the relative frequency column for Puerto Rico.

Destination Frequency Relative frequencyFlorida 26Mexico 78Belize 13Puerto Rico 28Alaska 2California 21Colorado 18Arizona 14A) 28 B) 0.14 C) 0.014 D) 0.28

43)

9

44) The data in the following table reflect the amount of time 40 students in a section of Statistics 101spend on homework each day. Find the value of the missing entry.

Homework time (minutes)

Relative frequency

0-14 0.0515-29 0.1030-44 0.2545-5960-74 0.1575-89 0.05

A) 40%B) 0.40C) 16D) The value cannot be determined from the given data.

44)

45) The data in the following table represent heights of students at a highschool. Find the value of themissing entry.

Height (centimeters)

Relative frequency

142 152 0.03 152 162 0.21 162 172 0.27 172 182 0.28 182 192 192 202 0.02A) 0.21B) 19%C) 0.19D) The value cannot be determined from the given data.

45)


Provide an appropriate response.46) When constructing a grouped-data table, what is the disadvantage of having too many

classes? What is the disadvantage of having too few classes?46)

47) Anna set up a grouped-data table with the following classes:

Number of sick days taken Frequency0-33-66-99-12

What is wrong with these classes? Describe two ways the classes could have been correctlydepicted.

47)

10

48) Suppose you are comparing frequency data for two different groups, 25 managers and 150blue collar workers. Why would a relative frequency distribution be better than afrequency distribution?

48)

Construct the specified histogram.49) The frequency table below shows the number of days off in a given year for 30 police

detectives.

Days off Frequency0 2 102 4 14 6 76 8 78 10 110 12 4

Construct a frequency histogram.

49)

11

Construct the requested histogram.50) The table gives the frequency distribution for the data involving the number of radios per

household for a sample of 80 U.S. households.

# of Radios Frequency 1 5 2 10 3 30 4 25 5 10

Construct a relative frequency histogram.

1 2 3 4 5

0.625

0.5

0.375

0.25

0.125

1 2 3 4 5

0.625

0.5

0.375

0.25

0.125

50)


Construct a dotplot for the given data.51) Attendance records at a school show the number of days each student was absent during the year.

The days absent for each student were as follows.9 3 4 2 8 6 3 4 0 6 7 3 4 2 2

A) B)

C) D)

51)

12

Construct a stem-and-leaf diagram for the given data.52) The diastolic blood pressures for a sample of patients at a clinic were as follows. The

measurements are in mmHg.

78 87 91 85 97 102 73 90 110 10594 85 81 95 77 106 84 111 83 9279 81 96 88 100 85 89 101 83 12088 95 78 74 105 85 87 92 114 83

A)789101112

8 3 7 9 8 4 7 5 5 1 4 3 1 8 5 9 3 8 5 7 3 1 7 0 4 5 2 6 5 2 2 5 6 0 1 5 0 1 4 0

B)

78910

8 3 7 9 8 4 7 5 5 1 4 3 1 8 5 9 3 8 5 7 3 1 7 0 4 5 2 6 5 2 2 0 5 6 1 0 1 5 4

52)

Construct a pie chart representing the given data set.53) The following figures give the distribution of land (in acres) for a county containing 88,000 acres.

Land Use Acres Relative FrequencyForest 13,200 0.15Farm 8800 0.10Urban 66,000 0.75

A) B)

53)

Construct the requested graph.

13

54) Construct a bar graph for the relative frequencies given.

Blood Frequency Relative type frequencyO 22 0.44A 19 0.38B 6 0.12AB 3 0.06

A)

B)

C)

54)

14

A nurse measured the blood pressure of each person who visited her clinic. Following is a relative -frequency histogramfor the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer thequestion. The blood pressure readings were given to the nearest whole number.

55) Approximately what percentage of the people aged 25-40 had a systolic blood pressure readingbetween 110 and 119 inclusive?

A) 0.35% B) 35% C) 3.5% D) 30%

55)

56) Approximately what percentage of the people aged 25-40 had a systolic blood pressure readingbetween 110 and 139 inclusive?

A) 74% B) 89% C) 59% D) 39%

56)

57) Approximately what percentage of the people aged 25-40 had a systolic blood pressure readinggreater than or equal to 130?

A) 26% B) 74% C) 23% D) 15%

57)

58) Approximately what percentage of the people aged 25-40 had a systolic blood pressure readingless than 120?

A) 3.5% B) 50% C) 35% D) 5%

58)

59) Given that 300 people were aged between 25 and 40, approximately how many had a systolicblood pressure reading between 140 and 149 inclusive?

A) 240 B) 2 C) 24 D) 8

59)

60) Given that 400 people were aged between 25 and 40, approximately how many had a systolicblood pressure reading of 140 or higher?

A) 11 B) 32 C) 44 D) 8

60)

61) Given that 200 people were aged between 25 and 40, approximately how many had a systolicblood pressure reading between 130 and 149 inclusive?

A) 5 B) 30 C) 46 D) 23

61)

62) Given that 200 people were aged between 25 and 40, approximately how many had a systolicblood pressure reading less than 130?

A) 15 B) 48 C) 148 D) 74

62)

15

63) Identify the midpoint of the third class.A) 120 B) 130 C) 125 D) 124

63)

64) What common class width was used to construct the frequency distribution?A) 11 B) 10 C) 100 D) 9

64)


Construct a relative-frequency polygon for the given data.65) The table contains the frequency and relative-frequency distributions for the ages of the

employees in a particular company department.

Age (years) Frequency Relative frequency 20 30 3 0.1875 30 40 6 0.375 40 50 4 0.25 50 60 1 0.0625 60 70 2 0.125

Relativefrequency

20 25 30 35 40 45 50 55 60 65 70

0.375

0.25

0.125

20 25 30 35 40 45 50 55 60 65 70

0.375

0.25

0.125

Age (years)

65)


Provide the requested response.66) The table contains data from a study of daily study time for 40 students from Statistics 101.

Construct an ogive from the data.

Minutes onhomework

Number of students

Relative frequency

Cumulative relative frequency

0 15 2 0.05 0.05 15 30 4 0.10 0.15 30 45 8 0.20 0.35 45 60 18 0.45 0.80 60 75 4 0.10 0.90 75 90 4 0.10 1.00

66)

16

A)

B)

C)

D) The table does not contain enough information to construct an ogive.

17

A graphical display of a data set is given. Identify the overall shape of the distribution as (roughly) bell -shaped,triangular, uniform, reverse J-shaped, J-shaped, right skewed, left skewed, bimodal, or multimodal.

67) A relative frequency histogram for the sale prices of homes sold in one city during 2006 is shownbelow.

A) J-shaped B) Reverse J-shapedC) Left skewed D) Right skewed

67)

68) A relative frequency histogram for the heights of a sample of adult women is shown below.

A) J-shaped B) Triangular C) Bell-shaped D) Left skewed

68)

18

69) A die was rolled 200 times and a record was kept of the numbers obtained. The results are shownin the relative frequency histogram below.

A) Left skewed B) J-shaped C) Triangular D) Uniform

69)

70) Two dice were rolled and the sum of the two numbers was recorded. This procedure was repeated400 times. The results are shown in the relative frequency histogram below.

A) Triangular B) Right-skewed C) Bell-shaped D) Left skewed

70)

71) The ages of a group of patients being treated at one hospital for osteoporosis are summarized inthe frequency histogram below.

A) Bell-shaped B) Reverse J-shapedC) Left skewed D) Right skewed

71)

19

72) A frequency histogram is given below for the weights of a sample of college students.

A) Multimodal B) Uniform C) Bell-shaped D) Bimodal

72)

A graphical display of a data set is given. State whether the distribution is (roughly) symmetric, right skewed, or leftskewed.

73) A relative frequency histogram for the sale prices of homes sold in one city during 2006 is shownbelow.

A) Left skewed B) Symmetric C) Right skewed

73)

20

74) A relative frequency histogram for the heights of a sample of adult women is shown below.

A) Symmetric B) Right skewed C) Left skewed

74)

75) A die was rolled 200 times and a record was kept of the numbers obtained. The results are shownin the relative frequency histogram below.

A) Symmetric B) Right skewed C) Left skewed

75)

76) Two dice were rolled and the sum of the two numbers was recorded. This procedure was repeated400 times. The results are shown in the relative frequency histogram below.

A) Right skewed B) Symmetric C) Left skewed

76)

21

77) The ages of a group of patients being treated at one hospital for osteoporosis are summarized inthe frequency histogram below.

A) Symmetric B) Left skewed C) Right skewed

77)

78) A frequency histogram is given below for the weights of a sample of college students.

A) Left skewed B) Symmetric C) Right skewed

78)


Provide an appropriate response.79) Hospital records show the age at death of patients who die while in the hospital. A

frequency histogram is constructed for the age at death of the people who have died at thehospital in the past five years. Roughly what shape would you expect for the distribution?Why?

79)


Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place thanthat used for the observations.

80) Last year, nine employees of an electronics company retired. Their ages at retirement are listedbelow. Find the mean retirement age.

50 62 6152 62 5865 52 55A) 57.4 yr B) 58.0 yr C) 56.2 yr D) 56.8 yr

80)

22

Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations.81) A sample of non-recyclable waste shipping companies in a certain state yielded the following

amounts, in tons, of waste shipped during 2005. Determine n, xi∑ , and x.

1192 419 878 739849 1101 512 1673453 654 791 843A) n = 12;

xi∑ = 10,104;

x = 918.5

B) n = 12;xi∑ = 10,104;

x = 842

C) n = 11;xi∑ = 10,104;

x = 842

D) n = 11;xi∑ = 10,104;

x = 918.5

81)

82) A scientist used the following data set showing the weight in pounds gained (or lost) by a sampleof eight laboratory animals given Drug X. Determine n, xi∑ , and x.

8.0 -7.3 2.5 3.0-2.4 2.4 5.0 -5.6

A) n = 10;xi∑ = 5.6;

x = 0.56

B) n = 8;xi∑ = 5.6;

x = 0.56

C) n = 8;xi∑ = 5.6;

x = 0.7

D) n = 10;xi∑ = 5.6;

x = 0.7

82)

Find the median for the given sample data.83) The salaries of ten randomly selected doctors are shown below.

$150,000 $143,000 $165,000 $238,000 $215,000$129,000 $139,000 $723,000 $217,000 $166,000

A) $165,500 B) $165,000 C) $229,000 D) $254,000

83)

Find the mode(s) for the given sample data.84) The blood types for 30 people who agreed to participate in a medical study were as follows.

O A A O A AB O B A OA O A B O O O AB A AA B O A A O O B O O

Find the mode of the blood types.A) O B) 13 C) O, A D) A

84)

85) Last year, nine employees of an electronics company retired. Their ages at retirement are listedbelow. Find the mode(s).

52 59 6055 51 6267 58 50A) 52, 59, 60, 55, 51, 62, 67, 58, 50 B) 57.1C) No mode D) 58

85)

23

Find the range for the given data.86) The weights, in pounds, of 18 randomly selected adults are given below.

120 165 187 143 119 132127 156 179 159 180 202114 146 151 168 173 144

A) 78 lbB) (114, 202) lbC) 202 lbD) (120, 202) lbE) 88 lb

86)

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than thatused for the observations.

87) 15, 42, 53, 7, 9, 12, 14, 28, 47A) 29.1 B) 16.6 C) 17.8 D) 15.8

87)

Find the range and standard deviation for each of the two samples, then compare the two sets of results.88) When investigating times required for drive-through service, the following results (in seconds)

were obtained.

Restaurant A 120 123 153 128 124 118 154 110Restaurant B 115 126 147 156 118 110 145 137A) Restaurant A: 46; 16.9

Restaurant B: 44; 16.2Both measures indicate there is more variation in the data for restaurant A than the data forrestaurant B.

B) Restaurant A: 44; 16.1Restaurant B: 46; 16.9Both measures indicate there is more variation in the data for restaurant B than the data forrestaurant A.

C) Restaurant A: 44; 16.2Restaurant B: 46; 16.9Both measures indicate there is more variation in the data for restaurant B than the data forrestaurant A.

D) Restaurant A: 46; 16.2Restaurant B: 44; 16.9It is inconclusive as to which data set has more variation.

88)

24

Provide an appropriate response.89) The manager of a bank recorded the amount of time each customer spent waiting in line during

peak business hours one Monday. The frequency distribution below summarizes the results. Findthe standard deviation. Round your answer to one decimal place.

Waiting time (minutes)

Number of customer

0 4 144 8 118 12 712 16 1616 20 020 24 2

A) 5.6 B) 5.3 C) 7.0 D) 5.9

89)

90) A companyʹs raw-data sample of weekly salaries (in dollars) is shown below.

230 340 320 590 780 980 600 350500 450 460 290 470 400 490 580570 890 680 410 860 540 530 690

A frequency distribution of this data set is presented below, with a third column showing the classmidpoints.

Salary Frequencyf

Midpointx

200 300300 400400 500500 600600 700700 800800 900900 1000

23663121

250350450550650750850950

(i) Use the raw data to obtain the sample standard deviation of the ungrouped data. Round youranswer to two decimal places.(ii) Use the grouped-data formula to obtain the sample standard deviation of the grouped data inthe frequency distribution. Round your answer to two decimal places.(iii) Compare your answers in parts (i) and (ii).

A) (i) The sample standard deviation of the ungrouped data is 194.48;(ii) The sample standard deviation of the grouped data is 194.48;(iii) The results in parts (i) and (ii) are the same. The grouped data formula will alwaysprovide the actual standard deviation when the data are grouped in classes each based on asingle value because the class midpoint is the same as each observation in each class.

B) (i) The sample standard deviation of the ungrouped data is 195.32;(ii) The sample standard deviation of the grouped data is 171.84;(iii) The results in parts (i) and (ii) are different. This discrepancy occurs because in thegrouped data formulas, every actual data value in a given class is replaced by the classmidpoint even though most values in the class are not equal to the midpoint.

90)

25

C) (i) The sample standard deviation of the ungrouped data is 171.84;(ii) The sample standard deviation of the grouped data is 171.84;(iii) The results in parts (i) and (ii) are the same. The grouped data formula will alwaysprovide the actual standard deviation when the data are grouped in classes each based on asingle value because the class midpoint is the same as each observation in each class.

D) (i) The sample standard deviation of the ungrouped data is 194.48;(ii) The sample standard deviation of the grouped data is 182.52;(iii) The results in parts (i) and (ii) are different. This discrepancy occurs because in thegrouped data formulas, every actual data value in a given class is replaced by the classmidpoint even though most values in the class are not equal to the midpoint.

Determine the quartile or interquartile range as specified.91) The weights (in pounds) of 17 randomly selected adults are given below. Find the interquartile

range.

144 165 187 143 119 132127 156 179 159 180 202114 146 151 168 173A) 37 lb B) 30 lb C) 37.5 lb D) 38 lb

91)

92) The weights (in pounds) of 18 randomly selected adults are given below. Find the third quartile,Q3 .

120 165 187 143 119 132127 156 179 159 180 202114 146 151 168 173 144A) 170.5 lb B) 173 lb C) 176 lb D) 174.5 lb

92)

Obtain the five-number summary for the given data.93) The normal annual precipitation (in inches) is given below for 21 different U.S. cities.

39.1 32.3 18.5 35.4 27.1 27.8 8.623.5 42.6 34.3 21.5 12.0 5.1 12.622.4 10.9 16.4 25.4 17.2 15.4 51.7

A) 5.1, 13.300, 22.4, 31.175, 51.7 inches B) 5.1, 14.00, 21.95, 33.30, 51.7 inchesC) 5.1, 15.4, 22.4, 32.3, 51.7 inches D) 5.1, 13.300, 21.95, 31.175, 51.7 inches

93)

Provide an appropriate response.94) Obtain the population standard deviation, σ, for the given data. Assume that the data represent

population data. Round your final answer to one more decimal place than that used for theobservations.

The number of years of teaching experience is given below for 12 high-school teachers.

26 27 28 28 12 1917 8 5 13 22 31

A) 69.1 yr B) 10.5 yr C) 8.3 yr D) 8.7 yr

94)

26

95) Following is the number of reported cases of influenza for two cities for the years 1996 through2005:

City A 1163 1954 1487 1864 1779 1244 1332 1299 1353 1802City B 937 1023 843 829 965 1011 943 831 976 858

(i) Without doing any calculations, decide for which city the standard deviation of the numbercases of influenza is larger. Explain.(ii) Find the individual population standard deviations of the number of cases of influenza. Roundyour final answer to two decimal places. Compare these answers with part (i).

A) (i) The range of the values for City A is 791, while it is only 192 for City B, so City A is likelyto have the larger standard deviation.(ii) City Aʹs population standard deviation is 277.40; City Bʹs population standard deviationis 71.29, so City A did have the larger standard deviation.

B) (i) The range of the values for City A is 767, while it is only 121 for City B, so City A is likelyto have the larger standard deviation.(ii) City Aʹs population standard deviation is 277.37; City Bʹs population standard deviationis 72.01, so City A did have the larger standard deviation.

C) (i) The range of the values for City A is 791, while it is only 192 for City B, so City A is likelyto have the larger standard deviation.(ii) City Aʹs population standard deviation is 278.43; City Bʹs population standard deviationis 71.25, so City A did have the larger standard deviation.

D) (i) The range of the values for City A is 767, while it is only 121 for City B, so City A is likelyto have the larger standard deviation.(ii) City Aʹs population standard deviation is 261.80; City Bʹs population standard deviationis 69.47, so City A did have the larger standard deviation.

95)

Solve the problem.96) Scores on a test have a mean of 72 and a standard deviation of 9. Michelle has a score of 81.

Convert Michelleʹs score to a z-score.A) -9 B) -1 C) 1 D) 9

96)

97) The mean of a set of data is 4.19 and its standard deviation is 2.77. Find the z-score for a value of12.32.Round your final answer to two decimal places.

A) 3.23 B) 3.24 C) 2.65 D) 2.94

97)

98) The mean of a set of data is -3.89 and its standard deviation is 3.83. Find the z-score for a value of5.58.Round your final answer to two decimal places.

A) 2.47 B) 2.77 C) 2.22 D) 2.72

98)

99) The mean of a set of data is 132.41 and its standard deviation is 71.48. Find the z-score for a valueof 319.06. Round your final answer to two decimal places.

A) 2.91 B) 2.61 C) 2.87 D) 2.35

99)

100) A variable x has a mean, μ, of 21.4 and a standard deviation, σ, of 5.1. Determine the z-scorecorresponding to an observed value for x of 20.4. Round your final answer to two decimal places.

A) -0.20 B) 8.20 C) 0.20 D) 0.71

100)

27

101) A meteorological office keeps records of the annual precipitation in different cities. For one city,the mean annual precipitation is 31.5 and the standard deviation of the annual precipitationamounts is 3.8. Let x represent the annual precipitation in that city. Determine the z-score for anannual precipitation in that city of 23.5 inches. Round your final answer to two decimal places.

A) 2.11 B) 14.47 C) 0.63 D) -2.11

101)

102) A variable x has a mean, μ, of 10 and a standard deviation, σ, of 7. Determine the standardizedversion of x.

A) x = z - 107

B) z = x - 107

C) z = - 107

D) z = x - 710

102)

103) A meteorological office keeps records of the annual precipitation in different cities. For one city,the mean annual precipitation is 15.3 and the standard deviation of the annual precipitationamounts is 4.2. Let x represent the annual precipitation in that city. Determine the standardizedversion of x.

A) z = x - 15.34.2

B) z = - 15.34.2

C) z = x - 4.215.3

D) x = z - 15.34.2

103)

104) A variable x has the possible observations shown below.

Possible observations of x: -3 -1 0 1 1 2 4 4 5Determine the standardized version of x.Round the values of μ and σ to one decimal place.

A) z = x - 1.42.6

B) x = z - 1.42.6

C) z = x - 2.51.4

D) z = x - 1.42.5

104)

105) A variable x has the possible observations shown below.

Possible observations of x: -3 -1 0 1 1 2 4 4 5

Find the z-score corresponding to an observed value of x of 5.Round the values of μ and σ to one decimal place. Round your final answer to two decimal places.

A) -1.44 B) -1.71 C) 1.44 D) 1.38

105)

Provide an appropriate response.106) Which score has a higher relative position, a score of 34.5 on a test with a mean of 30 and

a standard deviation of 3, or a score of 305.1 on a test with a mean of 270 and a a standarddeviation of 27? (Assume that the distributions being compared have approximately the sameshape.)

A) A score of 34.5B) A score of 305.1C) Both scores have the same relative position.

106)

28


Solve the problem.107) For a dayʹs work, Chris is paid $50 to cover expenses plus $16 per hour. Let x denote the

number of hours Chris works in a day and let y denote Chrisʹs total salary for the day.Obtain the equation that expresses y in terms of x. Construct a table of values using thex-values 2, 4, and 8 hours. Draw the graph of the equation by plotting the points from thetable and connecting them with a straight line. Use the graph to estimate visually Chrisʹssalary for the day if he works 6 hours.

x2 4 6 8

y

160

120

80

40

x2 4 6 8

y

160

120

80

40

107)


Determine the y-intercept and slope of the linear equation.108) y = 97.7 - 22.4x

A) y-intercept = -22.4, slope = 97.7 B) y-intercept = 97.7, slope = -22.4C) y-intercept = 22.4, slope = 97.7 D) y-intercept = 97.7, slope = 22.4

108)

You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or ishorizontal.

109) The equation of the line is y = -14 + 3.8x.A) Slopes downward B) Slopes upward C) Is horizontal

109)

110) The equation of the line is y = 10 - 12x.A) Is horizontal B) Slopes downward C) Slopes upward

110)

111) The equation of the line is y = 4.A) Slopes upward B) Slopes downward C) Is horizontal

111)

112) The y-intercept is -2 and the slope is 0.A) Slopes upward B) Slopes downward C) Is horizontal

112)

113) The y-intercept is -2.7 and the slope is 7.A) Slopes downward B) Is horizontal C) Slopes upward

113)

The y-intercept and slope, respectively, of a straight line are given. Find the equation of the line.114) 0 and -8.9

A) y = 8.9x B) y = 8.9 C) y = -8.9x D) y = -8.9114)

29

115) -2.7 and 0A) y = -2.7 B) y = 2.7 C) y = -2.7x D) y - 2.7x = 0

115)

116) -3 and -11A) y - 11x = -3 B) y = -3 + 11x C) y = -3 - 11x D) y = -3x - 11

116)

You are given information about a straight line. Use two points to graph the equation.117) The equation of the line is y = 7 - 0.5x.

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

117)

30

118) The equation of the line is y = 7.

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

118)

31

119) The y-intercept is -9 and the slope is 0.

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

119)

32

A set of data points and the equations of two lines are given. For each line, determine e2∑ . Then, determine which linefits the set of data points better, according to the least-squares criterion.

120) x 1 2 4 4y 2 3 5 4

Line A: y = 1 + 0.9xLine B: y = 0.8 + 1.1x

A) Line A: e2∑ = 0.57

Line B: e2∑ = 1.49Line A fits the set of data points better.

B) Line A: e2∑ = 0.57

Line B: e2∑ = 1.49Line B fits the set of data points better.

C) Line A: e2∑ = 1.31


D) Line A: e2∑ = 1.31


120)

121) x 0 1 3 3 5y 7 6 5 4 2

Line A: y = 7.5 - 0.9xLine B: y = 8.0 - 1.1x

A) Line A: e2∑ = 2.29


B) Line A: e2∑ = 0.87


C) Line A: e2∑ = 2.29


D) Line A: e2∑ = 3.12


121)

122) x 0 2 4 4 6 7y 1 4 9 11 14 15

Line A: y = 1.0 + 2.2xLine B: y = 1.2 + 2.1x

A) Line A: e2∑ = 6.04


B) Line A: e2∑ = 4.86


C) Line A: e2∑ = 6.04


D) Line A: e2∑ = 4.86


122)

Determine the regression equation for the data. Round the final values to three significant digits, if necessary.

123) x 2 4 5 6y 7 11 13 20

A) y^ = 3x B) y

^ = 0.15 + 3x C) y

^ = 2.8x D) y

^ = 0.15 + 2.8x

123)

33

124) x 0 3 4 5 12y 8 2 6 9 12

A) y^ = 4.98 + 0.425x B) y

^ = 4.88 + 0.525x

C) y^ = 4.98 + 0.725x D) y

^ = 4.88 + 0.625x

124)

125) x 6 8 20 28 36y 2 4 13 20 30

A) y^ = -2.79 + 0.897x B) y

^ = -3.79 + 0.897x

C) y^ = -3.79 + 0.801x D) y

^ = -2.79 + 0.950x

125)

126) x 3 5 7 15 16y 8 11 7 14 20

A) y^ = 5.07 + 0.850x B) y

^ = 4.07 + 0.753x

C) y^ = 4.07 + 0.850x D) y

^ = 5.07 + 0.753x

126)

127) x 24 26 28 30 32y 15 13 20 16 24

A) y^ = -11.8 + 0.950x B) y

^ = 11.8 + 1.05x

C) y^ = -11.8 + 1.05x D) y

^ = 11.8 + 0.950x

127)

128) x 1 3 5 7 9y 143 116 100 98 90

A) y^ = 151 - 6.8x B) y

^ = -140 + 6.2x C) y

^ = -151 + 6.8x D) y

^ = 140 - 6.2x

128)

129) x 1.2 1.4 1.6 1.8 2.0y 54 53 55 54 56

A) y^ = 50 + 3x B) y

^ = 50.4 + 2.5x C) y

^ = 54 D) y

^ = 55.3 + 2.4x

129)

130) Ten students in a graduate program were randomly selected. The following data represent theirgrade point averages (GPAs) at the beginning of the year (x) versus their GPAs at the end of theyear (y).

x y3.5 3.63.8 3.73.6 3.93.6 3.63.5 3.93.9 3.84.0 3.73.9 3.93.5 3.83.7 4.0

A) y^ = 2.51 + 0.329x B) y

^ = 4.91 + 0.0212x

C) y^ = 5.81 + 0.497x D) y

^ = 3.67 + 0.0313x

130)

34

131) Two different tests are designed to measure employee productivity (x) and dexterity (y). Severalemployees were randomly selected and tested, and the results are given below.

xy 23 25 28 21 21 25 26 30 34 3649 53 59 42 47 53 55 63 67 75

A) y^ = 5.05 + 1.91x B) y

^ = 75.3 - 0.329x

C) y^ = 10.7 + 1.53x D) y

^ = 2.36 + 2.03x

131)

132) Managers rate employees according to job performance (x) and attitude (y). The results for severalrandomly selected employees are given below.

xy 59 63 65 69 58 77 76 69 70 6472 67 78 82 75 87 92 83 87 78

A) y^ = 92.3 - 0.669x B) y

^ = -47.3 + 2.02x

C) y^ = 2.81 + 1.35x D) y

^ = 11.7 + 1.02x

132)

The regression equation for the given data points is provided. Graph the regression equation and the data points.

133) x 2 4 5 6y 7 11 13 20

y^ = 3.0x

x2 4 6

y

18

12

6

x2 4 6

y

18

12

6

A)

x2 4 6

y

18

12

6

x2 4 6

y

18

12

6

B)

x2 4 6

y

18

12

6

x2 4 6

y

18

12

6

133)

35

C)

x2 4 6

y

18

12

6

x2 4 6

y

18

12

6

D)

x2 4 6

y

18

12

6

x2 4 6

y

18

12

6

134) x 3 5 7 15 16y 8 11 7 14 20

y^ = 5.1 + 0.75x

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

A)

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

B)

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

134)

36

C)

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

D)

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

x2 4 6 8 10 12 14 16 18 20

y21

18

15

12

9

6

3

135) x 1 3 5 7 9y 73 46 30 28 20

y^= 70.4 - 6.2x

x1 2 3 4 5 6 7 8 9

y100908070605040302010

x1 2 3 4 5 6 7 8 9

y100908070605040302010

A)

x1 2 3 4 5 6 7 8 9

y100908070605040302010

x1 2 3 4 5 6 7 8 9

y100908070605040302010

B)

x1 2 3 4 5 6 7 8 9

y100908070605040302010

x1 2 3 4 5 6 7 8 9

y100908070605040302010

135)

37

C)

x1 2 3 4 5 6 7 8 9

y100908070605040302010

x1 2 3 4 5 6 7 8 9

y100908070605040302010

D)

x1 2 3 4 5 6 7 8 9

y100908070605040302010

x1 2 3 4 5 6 7 8 9

y100908070605040302010

136) x 10 14 20 6 6 14 16 24 32 36 y 19 23 29 12 17 23 25 33 37 45

y^= 9.3 + 0.95x

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

A)

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

B)

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

136)

38

C)

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

D)

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

x4 8 12 16 20 24 28 32 36 40

y

40

30

20

10

Use the regression equation to predict the y-value corresponding to the given x-value. Round your answer to the nearesttenth.

137) Eight pairs of data yield the regression equation y^ = 55.8 + 2.79x. Predict y for x = 5.2.

A) 57.8 B) 293.0 C) 71.1 D) 70.3137)

138) Nine pairs of data yield the regression equation y^= 19.4 + 0.93x. Predict y for x = 54.

A) 64.7 B) 79.6 C) 69.6 D) 57.8138)

139) The regression equation relating dexterity scores (x) and productivity scores (y) for ten randomly

selected employees of a company is y^ = 5.50 + 1.91x. Predict the productivity score for an employee

whose dexterity score is 32.A) 56.3 B) 58.2 C) 177.9 D) 66.6

139)

140) The regression equation relating attitude rating (x) and job performance rating (y) for ten

randomly selected employees of a company is y^ = 11.7 + 1.02x. Predict the job performance rating

for an employee whose attitude rating is 67.A) 12.6 B) 80.0 C) 78.9 D) 80.1

140)

Compute the specified sum of squares.141) The regression equation for the data below is y

^ = 3.000x.

x 2 4 5 6y 7 11 13 20

SSRA) 78.75 B) 72.45 C) 10.00 D) 88.75

141)

142) The data below consist of test scores (y) and hours of preparation (x) for 5 randomly selected

students. The regression equation is y^ = 44.8447 + 3.52427x.

x 5 2 9 6 10y 64 48 72 73 80

SSRA) 511.724 B) 87.4757 C) 599.200 D) 498.103

142)

39

143) The data below consist of heights (x), in meters, and masses (y), in kilograms, of 6 randomly

selected adults. The regression equation is y^ = -181.342 + 144.46x.

x 1.61 1.72 1.78 1.80 1.67 1.88y 54 62 70 84 61 92

SSRA) 1079.5 B) 979.44 C) 1149.2 D) 100.06

143)

144) The regression equation for the data below is y^ = 6.18286 + 4.33937x.

x 9 7 2 3 4 22 17y 43 35 16 21 23 102 81

SSRA) 13.4790 B) 6544.86 C) 6531.37 D) 6421.83

144)

145) The regression equation for the data below is y^ = 3.000x.

x 2 4 5 6y 7 11 13 20

SSEA) 10.00 B) 88.75 C) 78.75 D) 14.25

145)



x 5 2 9 6 10y 64 48 72 73 80

SSEA) 511.724 B) 599.200 C) 87.4757 D) 96.1030

146)



x 1.61 1.72 1.78 1.80 1.67 1.88y 54 62 70 84 61 92

SSEA) 119.30 B) 979.44 C) 100.06 D) 1079.5

147)

40

148) The regression equation for the data below is y^ = 3.000x.

x 2 4 5 6y 7 11 13 20

SSTA) 10.00 B) 78.75 C) 92.25 D) 88.75

148)



x 5 2 9 6 10y 64 48 72 73 80

SSTA) 599.200 B) 498.103 C) 511.724 D) 87.4757

149)



x 1.61 1.72 1.78 1.80 1.67 1.88y 54 62 70 84 61 92

SSTA) 100.06 B) 1079.5 C) 979.44 D) 1119.3

150)

Compute the coefficient of determination. Round your answer to four decimal places.151) A regression equation is obtained for a set of data points. It is found that the total sum of squares is

26.961, the regression sum of squares is 15.044, and the error sum of squares is 11.917.A) 1.7921 B) 0.7921 C) 0.4420 D) 0.5580

151)

152) A regression equation is obtained for a set of data points. It is found that the total sum of squares is117.0, the regression sum of squares is 81.5, and the error sum of squares is 35.5.

A) 0.3034 B) 0.6966 C) 0.4356 D) 1.4356

152)

153) The regression equation for the data below is y^ = 3x.

x 2 4 5 6y 7 11 13 20

A) 0.4839 B) 0.9420 C) 0.8873 D) 0.7265

153)

154) The test scores (y) of 6 randomly selected students and the numbers of hours they prepared (x) areas follows.

x 5 10 4 6 10 9y 64 86 69 86 59 87

The regression equation is y^ = 1.06604x + 67.3491.

A) -0.2242 B) 0.2242 C) 0.6781 D) 0.0503

154)

41

155) The cost of advertising (x), in thousands of dollars, and the number of products sold (y), inthousands, for eight randomly selected product lines are shown below.

x 9 2 3 4 2 5 9 10y 85 52 55 68 67 86 83 73

The regression equation is y^ = 2.78846x + 55.7885.

A) 0.5009 B) -0.0707 C) 0.2353 D) 0.7077

155)

156) For a particular regression analysis, it is found that SST = 895.0 and SSE = 352.2.A) 0.6065 B) 0.3935 C) 0.7788 D) 2.5412

156)

Determine the percentage of variation in the observed values of the response variable that is explained by theregression. Round to the nearest tenth of a percent if needed.

157) x 16.9 34.2 44.8 11.9 18.3y 2 7 4 10 2A) 12.8% B) 1.4% C) 10.5% D) 11.8%

157)

158) x 5 10 4 6 10 9y 64 86 69 86 59 87A) 5.0% B) 22.4% C) 0% D) 67.8%

158)

159) x 9 2 3 4 2 5 9 10y 85 52 55 68 67 86 83 73A) 70.8% B) 50.1% C) 23.5% D) 24.6%

159)

Solve the problem.160) The paired data below consist of the temperatures on randomly chosen days and the amount a

certain kind of plant grew (in millimeters): x 62 76 50 51 71 46 51 44 79y 36 39 50 13 33 33 17 6 16

Find the SST.A) 1684 B) 243 C) 0 D) 1864

160)

161) The paired data below consist of the temperatures on randomly chosen days and the amount acertain kind of plant grew (in millimeters): x 62 76 50 51 71 46 51 44 79y 36 39 50 13 33 33 17 6 16

Find the SSR.A) 242.951 B) 64.328 C) 243 D) 0

161)

162) The paired data below consist of the temperatures on randomly chosen days and the amount acertain kind of plant grew (in millimeters): x 62 76 50 51 71 46 51 44 79y 36 39 50 13 33 33 17 6 16

Find the SSE.A) 243 B) 242.951 C) 1619.672 D) 1748.328

162)

42

163) A study was conducted to compare the average time spent in the lab each week versus coursegrade for computer students. The results are recorded in the table below. Number of hours spent in lab Grade (percent)

10 9611 5116 629 587 8915 8116 4610 51

Find the coefficient of determination.A) 0.462 B) 0.335 C) 0.017 D) 0.112

163)


10 9611 5116 629 587 8915 8116 4610 51

Determine the percentage of variation in the observed values of the response variable explained bythe regression..

A) 0.335% B) 0.112% C) 33.5% D) 11.2%

164)


10 9611 5116 629 587 8915 8116 4610 51

State how useful the regression equation appears to be for making predictions.A) Not very useful B) Extremely usefulC) Moderately useful D) Not enough information

165)

43


Provide an appropriate response.166) For a particular regression analysis, the following regression equation is obtained:

y^ = 2.12 + 0.56x. Furthermore, the coefficient of determination is 0.024. How useful wouldthe regression equation be for making predictions? How can you tell?

166)


167) True or false? In the context of regression analysis, the coefficient of determination is theproportion of variation in the observed values of the response variable not explained by theregression

A) True B) False

167)

168) True or false? In the context of regression analysis, the regression sum of squares is the variation inthe observed values of the response variable explained by the regression.

A) True B) False

168)


169) For a particular regression analysis, it is found that SST = 924.5 and SSE = 807.5. Does theregression equation appear to be useful for making predictions? How can you tell?

169)


170) True or false? In the context of regression analysis, if the regression sum of squares is large relativeto the error sum of squares, then the regression equation is useful for making predictions.

A) True B) False

170)


171) When performing regression analysis, how can you evaluate how useful the regressionequation is for making predictions?

171)


172) For a particular regression analysis, the following regression equation is obtained: y^ = 8.3x + 32,

where x represents the number of hours studied for a test and y represents the score on the test.True or false? If the coefficient of determination is 0.976, the number of hours studied is very usefulfor predicting the test score.

A) True B) False

172)

Obtain the linear correlation coefficient for the data. Round your answer to three decimal places.

173) x 34.0 22.4 10.8 38.3 31.3y 8 6 5 7 2A) 0.249 B) -0.249 C) 0 D) -0.222

173)

174) x 57 53 59 61 53 56 60y 156 164 163 177 159 175 151A) 0.109 B) -0.078 C) -0.054 D) 0.214

174)

44

175) x 62 53 64 52 52 54 58y 158 176 151 164 164 174 162A) 0.507 B) 0.754 C) -0.081 D) -0.775

175)

176) The data below show the test scores (y) of 6 randomly selected students and the number of hours(x) they studied for the test.

x 5 10 4 6 10 9y 64 86 69 86 59 87A) 0.678 B) -0.678 C) 0.224 D) -0.224

176)

177) The data below show the cost of advertising (x), in thousands of dollars, and the number ofproducts sold (y), in thousands, for each of eight randomly selected product lines.

x 9 2 3 4 2 5 9 10 y 85 52 55 68 67 86 83 73A) 0.246 B) -0.071 C) 0.235 D) 0.708

177)

178) A study was conducted to compare the number of hours spent in the computer lab on anassignment (x) and the grade on the assignment (y), for each of eight randomly selected studentsin a computer class. The results are recorded in the table below.

x y10 9611 5116 62 9 58 7 8915 8116 4610 51

A) -0.284 B) 0.462 C) 0.017 D) -0.335

178)

179) Managers rate employees according to job performance (x) and attitude (y). The results for severalrandomly selected employees are given below.

xy 59 63 65 69 58 77 76 69 70 6472 67 78 82 75 87 92 83 87 78A) 0.863 B) 0.610 C) 0.729 D) 0.916

179)

180) Two separate tests, x and y, are designed to measure a studentʹs ability to solve problems. Severalstudents are randomly selected to take both tests and their results are shown below.

x 48 52 58 44 43 43 40 51 59y 73 67 73 59 58 56 58 64 74A) 0.714 B) 0.109 C) 0.867 D) 0.548

180)

45

181) The data below show the temperature (x) and the amount a plant grew (y), in millimeters, for eachof nine randomly selected days. Calculate the linear correlation coefficient r. Can you concludefrom the value of r alone that the variables x and y are unrelated?

x 62 76 50 51 71 46 51 44 79 y 36 39 50 13 33 33 17 6 16A) 0.196; Yes B) 0.196; No C) 0.038; No D) 0.038; Yes

181)

182) Two different tests are designed to measure employee productivity (x) and dexterity (y). Severalemployees are randomly selected and tested with these results. Calculate the linear correlationcoefficient r. Can you conclude from the value of r alone that the variables x and y are linearlyrelated?

xy 23 25 28 21 21 25 26 30 34 3649 53 59 42 47 53 55 63 67 75A) 0.986; Yes B) 0.986; No C) 0.972 No D) 0.972;Yes

182)

Provide an appropriate response.183) Determine which plot shows the strongest linear correlation.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

183)

46


184) What is the relationship between the linear correlation coefficient and the usefulness of theregression equation for making predictions?

184)

185) Create a scatter diagram that shows a perfect positive linear correlation between x and y.How would the scatter diagram change if the correlation showed each of the following?(a) a strong positive linear correlation;(b) a weak positive linear correlation;(c) no linear correlation.

185)

186) Suppose data are collected for each of several randomly selected adults for height, ininches, and number of calories burned in 30 minutes of walking on a treadmill at 3.5 mph.How would the value of the linear correlation coefficient, r, change if all of the heightswere converted to meters?

186)

187) Explain why having a high linear correlation does not imply causality. Give an example tosupport your answer.

187)

188) The variables height and weight could reasonably be expected to have a positive linearcorrelation coefficient, since taller people tend to be heavier, on average, than shorterpeople. Give an example of a pair of variables which you would expect to have a negativelinear correlation coefficient and explain why. Then give an example of a pair of variableswhose linear correlation coefficient is likely to be close to zero.

188)


189) Which of the following statements concerning the linear correlation coefficient are true?

A: If the linear correlation coefficient for two variables is zero, then there is no relationshipbetween the variables.

B: If the slope of the regression line is negative, then the linear correlation coefficient is negative.

C: The value of the linear correlation coefficient always lies between -1 and 1.

D: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linearcorrelation coefficient of -0.82.

A) A and D B) A and B C) C and D D) B and C

189)


190) For each of 200 randomly selected cities, Pete compared data for the number of churchesin the city (x) and the number of homicides in the past decade (y). He calculated the linearcorrelation coefficient and was surprised to find a strong positive linear correlation for thetwo variables. Does this suggest that when a city builds new churches this will tend tocause an increase in the number of homicides? Why do you think that a strong positivelinear correlation coefficient was obtained?

190)

47


Find the indicated probability.191) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH

TTT. What is the probability of getting at least one head?

A) 14

B) 78

C) 12

D) 34

191)

192) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTHTTT. What is the probability of getting at least two tails?

A) 12

B) 18

C) 58

D) 38

192)

193) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH,TTT. What is the probability that the first two tosses come up the same?

A) 14

B) 38

C) 12

D) 18

193)

194) If two balanced die are rolled, the possible outcomes can be represented as follows.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Determine the probability that the sum of the dice is 9.

A) 19

B) 16

C) 112

D) 536

194)

195) If two balanced die are rolled, the possible outcomes can be represented as follows.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Determine the probability that the sum of the dice is 4 or 10.

A) 536

B) 736

C) 29

D) 16

195)

48

196) A committee of three people is to be formed. The three people will be selected from a list of fivepossible committee members. A simple random sample of three people is taken, withoutreplacement, from the group of five people. If the five people are represented by the letters A, B, C,D, E, the possible outcomes are as follows.

ABCABDABEACDACEADEBCDBCEBDECDE

Determine the probability that C and D are both included in the sample.

A) 25

B) 310

C) 110

D) 210

196)

197) A committee of three people is to be formed. The three people will be selected from a list of fivepossible committee members. A simple random sample of three people is taken, withoutreplacement, from the group of five people. Using the letters A, B, C, D, E to represent the fivepeople, list the possible samples of size three and use your list to determine the probability that Bis included in the sample.

(Hint: There are 10 possible samples.)

A) 710

B) 12

C) 35

D) 25

197)

198) Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick.Simultaneously, they take out a single food item and consume it. The possible pairs of food itemsthat Sally and Sammy consumed are as follows.

chocolate bar - chocolate barlicorice stick - chocolate barbanana - bananachocolate bar - licorice sticklicorice stick - licorice stickchocolate bar - bananabanana - licorice sticklicorice stick - bananabanana - chocolate bar

Find the probability that at least one chocolate bar was eaten.

A) 45

B) 79

C) 59

D) 13

198)

49

199) A bag contains four chips of different colors, including red, blue, green, and yellow. A chip isselected at random from the bag and then replaced in the bag. A second chip is then selected atrandom. Make a list of the possible outcomes (for example RB represents the outcome red chipfollowed by blue chip) and use your list to determine the probability that the two chips selectedare the same color.

(Hint: There are 16 possible outcomes.)

A) 14

B) 18

C) 116

D) 12

199)

200) A bag contains four chips of different colors, including red, blue, green, and yellow. A chip isselected at random from the bag and then replaced in the bag. A second chip is then selected atrandom. Make a list of the possible outcomes (for example RB represents the outcome red chipfollowed by blue chip) and use your list to determine the probability that one blue chip and oneyellow chip are selected.

A) 18

B) 12

C) 116

D) 14

200)

Estimate the probability of the event.201) A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum,

obtained the set of survey responses to make its estimate. The encoding system for the data is:1 = FOR, 2 = AGAINST. If the referendum were held today, find the probability that it would pass.

1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1A) 0.6 B) 0.65 C) 0.5 D) 0.4

201)

202) The data set represents the income levels of the members of a country club. Find the probabilitythat a randomly selected member earns at least $92,000. Round your answers to the nearest tenth.

98,000 104,000 84,000 107,000 88,000 98,000 92,000 76,000 113,000 128,000 80,000 95,000 110,00088,000 104,000 101,000 92,000 116,000 72,000 101,000

A) 0.8 B) 0.4 C) 0.7 D) 0.6

202)

203) In a certain class of students, there are 10 boys from Wilmette, 5 girls from Kenilworth, 10 girlsfrom Wilmette, 7 boys from Glencoe, 5 boys from Kenilworth and 6 girls from Glencoe. If theteacher calls upon a student to answer a question, what is the probability that the student will befrom Kenilworth?

A) 0.116 B) 0.233 C) 0.313 D) 0.227

203)

204) The following frequency distribution analyzes the scores on a math test. Find the probability that ascore greater than 82 was achieved.

A) 0.813 B) 0.625 C) 0.188 D) 0.375

204)

50

205) A frequency distribution on employment information from Alpha Corporation follows.. Find theprobability that an employee has been with the company 10 years or less.

Years Employed No. of Employees 1-5 5 6-10 20 11-15 25 16-20 10 21-25 5 26-30 3

A) 0.368 B) 0.294 C) 0.735 D) 0.632

205)

Answer the question.206) Find the odds against correctly guessing the answer to a multiple choice question with 5 possible

answers.A) 4 to 1 B) 5 to 1 C) 5 to 4 D) 4 to 5

206)

207) In a certain town, 25% of people commute to work by bicycle. If a person is selected randomlyfrom the town, what are the odds against selecting someone who commutes by bicycle?

A) 1 to 4 B) 3 to 4 C) 3 to 1 D) 1 to 3

207)

208) Suppose you are playing a game of chance. If you bet $4 on a certain event, you will collect $92(including your $4 bet) if you win. Find the odds used for determining the payoff.

A) 23 to 1 B) 22 to 1 C) 1 to 22 D) 92 to 96

208)


Provide an appropriate response.209) Discuss the range of possible values for probabilities. Give examples to support each. 209)

210) On an exam question asking for a probability, Sue had an answer of 138. Explain how she

knew that this result was incorrect.

210)

211) Describe an event whose probability of occurring is 1 and explain what that probabilitymeans. Describe an event whose probability of occurring is 0 and explain what thatprobability means.

211)


212) Which of the following could not possibly be probabilities?

A. -0.31

B. 87

C. 0D. 0.71

A) A and C B) A and B C) A and D D) B and C

212)

51

213) When a balanced die is rolled, the probability that the number that comes up will be a one is 16.

This means that if the die is rolled 36 times, a one will show up six times.A) True B) False

213)


214) Interpret the following probability statement using the frequentist interpretation ofprobability. The probability is 0.83 that this particular type of surgery will be successful.

214)

215) Suppose that you roll a die and record the number that comes up and then flip a coin andrecord whether it comes up heads or tails. One possible outcome can be represented as 2H(a two on the die followed by heads). Make a list of all the possible outcomes. What is theprobability that you get tails and an even number? What assumption are you makingwhen you find this probability?

215)

216) Suppose that in an election for governor of Oregon there are five candidates of whom twoare women. A statistics student reasons as follows. The probability that a woman will win

the election is equal to fN which is 2

5. What is wrong with his reasoning?

216)


List the outcomes comprising the specified event.217) Three board members for a nonprofit organization will be selected from a group of five people.

The board members will be selected by drawing names from a hat. The names of the five possibleboard members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can berepresented as follows.

ABC ABD ABE ACD ACEADE BCD BCE BDE CDE

Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to beon the board. List the outcomes that comprise the following event.

A = event that Charlie is selectedA) ABC, ACD, ACE, BCD, BCE, CDE B) ABC, ACD, ACE, BCD, CDEC) CDE D) ABC, ACD, ACE, BCD, BCE, CDE, BDE

217)

52

218) When a quarter is tossed four times, 16 outcomes are possible.

HHHH HHHT HHTH HHTTHTHH HTHT HTTH HTTTTHHH THHT THTH THTTTTHH TTHT TTTH TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tossesare tails, and the fourth toss is heads. List the outcomes that comprise the following event.

A = event the first three tosses come up the sameA) HHHT, TTTH B) HHHH, HHHT, TTTH, TTTTC) HHHT, TTTH, HTTT, THHH D) HHH, TTT

218)

219) In a competition, two people will be selected from four finalists to receive the first and secondprizes. The prize winners will be selected by drawing names from a hat. The names of the fourfinalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows.

JG JH JM GJ GH GMHJ HG HM MJ MG MH

Here, for example, JG represents the outcome that Jim receives the first prize and George receivesthe second prize. List the outcomes that comprise the following event.

A = event that both prize winners are womenA) HJ, HM, MH B) HM, MH, HG, MGC) HM D) HM, MH

219)

List the outcome(s) of the stated event.220) The odds against winning in a horse race are shown in the following table.

Horse #1 #2 #3 #4 #5 #6 #7Odds 8 16 1 20 10 16 20

Based on these odds, which horses comprise: A = event one of the top two favorites wins the race?A) Horses #4 and #7 B) Horses #1 and #2C) Horse #3 D) Horses #1 and #3

220)

221) The odds against winning in a horse race are shown in the following table.

Horse #1 #2 #3 #4 #5 #6 #7Odds 2 16 2 18 9 18 5

Based on these odds, which horses comprise: A = event one of the two long shots (least likely towin) wins the race?

A) Horses #4 and #6 B) Horse #1C) Horses #1 and #2 D) Horses #1 and #3

221)

53

222) The odds against winning in a horse race are shown in the following table.

Horse #1 #2 #3 #4 #5 #6 #7Odds 8 14 1 18 12 18 1

Based on these odds, which horses comprise: A = event the winning horseʹs number is above 4?A) Horses #1, #2, #4, #5, and #6 B) Horses #5, #6, and #7C) Horses #4, #5, #6, and #7 D) Horse #7

222)

List the outcomes comprising the specified event.223) When a quarter is tossed four times, 16 outcomes are possible.


Here, for example, HTTH represents the outcome that the first toss is heads, the next two tossesare tails, and the fourth toss is heads. The event A is defined as follows.

A = event the first two tosses are heads

List the outcomes that comprise the event (not A).A) HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTTB) HHHH, HHHT, HHTH, HHTTC) TTHH, TTHT, TTTH, TTTTD) THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT

223)



Here, for example, HTTH represents the outcome that the first toss is heads, the next two tossesare tails, and the fourth toss is heads. The events A and B are defined as follows.

A = event exactly two tails are tossedB = event the first and last tosses are the same

List the outcomes that comprise the event (A & B).A) HTTH, THHTB) HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTTC) HHTT, HTHT, HTTH, THHT, THTH, TTHHD) HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTT

224)

54




A = event exactly two tails are tossedB = event the first and last tosses are the same

List the outcomes that comprise the event (A or B).A) HTTH, THHTB) HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTTC) HHTT, HTHT, HTTH, THHT, THTH, TTHHD) HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT

225)

226) Three board members for a nonprofit organization will be selected from a group of five people.The board members will be selected by drawing names from a hat. The names of the five possibleboard members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can berepresented as follows.


Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be onthe board. The event A is defined as follows.

A = event that Bob and Dave are both selected

List the outcomes that comprise the event (not A).A) ABC, ABE, ACD, ACE, ADE, BCE, CDE B) ABC, ABE, ACE, ADE, BCE, CDEC) ABD, BCD, BDE D) ACE

226)

55

227) Three board members for a nonprofit organization will be selected from a group of five people.The board members will be selected by drawing names from a hat. The names of the five possibleboard members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can berepresented as follows.


Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be onthe board. The events A and B are defined as follows.

A = event that Dave is selectedB = event that fewer than two men are selected

List the outcomes that comprise the event (A & B).A) ABD, ADE, BDE, ABC, ACE, BCE B) ABE, ABD, ADE, BDEC) ABD, ADE, BDE, BCD, ACD, CDE D) ABD, ADE, BDE

227)

228) Three board members for a nonprofit organization will be selected from a group of five people.The board members will be selected by drawing names from a hat. The names of the five possibleboard members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can berepresented as follows.


Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to beon the board. The events A and B are defined as follows.

A = event that Dave is selectedB = event that Allison is selected

List the outcomes that comprise the event (A or B).A) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BDEB) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BDE, CDEC) ABD, ACD, ADED) ABC, ABE, ACE, BCD, BDE, CDE

228)

56



Here, for example, JG represents the outcome that Jim receives the first prize and George receivesthe second prize. The event A is defined as follows.

A = event that Helen gets first prize

List the outcomes that comprise the event (not A).A) JG, JH, JM, GJ, GH, GM, MJ B) JG, JM, GJ, GM, MJ, MGC) HJ, HG, HM D) JG, JH, JM, GJ, GH, GM, MJ, MG, MH

229)



Here, for example, JG represents the outcome that Jim receives the first prize and George receivesthe second prize. The events A and B are defined as follows.

A = event that Helen gets first prizeB = event that George gets a prize

List the outcomes that comprise the event (A or B).A) HGB) JG, GJ, GH, GM, HJ, HM, MGC) JG, GJ, GH, GM, HJ, HG, HM, MGD) JG, JH, GJ, GH, GM, HJ, HG, HM, MG, MH

230)



Here, for example, JG represents the outcome that Jim receives the first prize and George receivesthe second prize. The events A and B are defined as follows.

A = event that Helen gets first prizeB = event that both prize winners are women

List the outcomes that comprise the event (A & B).A) HJ, HG, HM B) HJ, HG, HM, MHC) HM D) HM, MH

231)

57

Describe the specified event in words.232) The number of hours needed by sixth grade students to complete a research project was recorded

with the following results. Hours Number of students (f)4 155 116 197 68 99 16

10 2

A student is selected at random. The event A is defined as follows.

A = the event the student took at least 8 hours

Describe the event (not A) in words.A) The event the student took at most 8 hoursB) The event the student took more than 8 hoursC) The event the student took less than 8 hoursD) The event the student did not take 8 hours

232)

233) The number of hours needed by sixth grade students to complete a research project was recordedwith the following results. Hours Number of students (f)4 155 116 197 68 99 1610 2


A = the event the student took between 5 and9 hours inclusive

B = the event the student took at least 7 hours

Describe the event (A & B) in words.A) The event the student took between 5 and 7 hours inclusiveB) The event the student took between 7 and 9 hours inclusiveC) The event the student at least 5 hoursD) The event the student took more than 7 hours and less than 9 hours

233)

58

234) The number of hours needed by sixth grade students to complete a research project was recordedwith the following results. Hours Number of students (f)4 55 116 197 68 99 16

10 2

A student is selected at random. The events A and B are defined as follows.

A = the event the student took less than 10 hoursB = the event the student took between 9 and

5 hours inclusive

Describe the event (A or B) in words.A) The event the student took between 10 and 9 hours inclusiveB) The event the student took less than 10 hours or more than 9 hoursC) The event the student took less than 10 hours or between 9 and 5 hours inclusiveD) The event the student took less than 10 hours and between 9 and 5 hours inclusive

234)

Determine the number of outcomes that comprise the specified event.235) The age distribution of students at a community college is given below.

Age (years) Number of students (f)Under 21 204121-25 211826-30 116731-35 845Over 35 226

A student from the community college is selected at random. The event A is defined as follows.

A = event the student is between 26 and 35 inclusive.

Determine the number of outcomes that comprise the event (not A).A) 4159 B) 2012 C) 4385 D) 5230

235)

59

236) The age distribution of students at a community college is given below. Age (years) Number of students (f)Under 21 206321-25 214226-30 115831-35 880Over 35 204

A student from the community college is selected at random. The event A is defined as follows.

A = event the student is under 31


236)


A student from the community college is selected at random. The events A and B are defined asfollows.

A = event the student is between 21 and 35 inclusiveB = event the student is 26 or over

Determine the number of outcomes that comprise the event (A & B).A) 6302 B) 4291 C) 2011 D) 2234

237)



A = event the student is under 21B = event the student is over 35


238)

60



A = event the student is between 21 and 35 inclusiveB = event the student is 26 or over

Determine the number of outcomes that comprise the event (A or B).A) 1851 B) 4107 C) 5958 D) 2054

239)


10+ 7




240)

61


10+ 5


A = the event the student took more than 7 hours


241)


10+ 5


A = the event the student took at most 8 hoursB = the event the student took at least 8 hours


242)

62


10+ 5


A = the event the student took at most 8 hoursB = the event the student took at least 8 hours


243)

244) The number of hours needed by sixth grade students to complete a research project was recordedwith the following results. Hours Number of students (f)4 225 296 237 148 119 810+ 6



B = the event the student took at most 7 hours


244)

63

Determine whether the events are mutually exclusive.245) When a quarter is tossed four times, 16 outcomes are possible.



A = event the first two tosses are headsB = event the first and last tosses are the same

Are the events A and B mutually exclusive?A) Yes B) No

245)




A = event exactly two heads are tossedB = event all four tosses come up the same


246)



Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to beon the board. The events A and B are defined as follows.

A = event that Betty and Allison are both selectedB = event that more than one man is selected


247)

64



Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to beon the board. The events A, B, and C are defined as follows.

A = event that Dave and Allison are both selectedB = event that more than one man is selectedC = event that fewer than two women are selected

Is the collection of events A, B, and C mutually exclusive?A) Yes B) No

248)

249) A card is selected randomly from a deck of 52. The events A, B, and C are defined as follows.

A = event the card selected is a heartB = event the card selected is a clubC = event the card selected is an ace


249)

250) The number of hours needed by sixth grade students to complete a research project was recordedwith the following results. Hours Number of students (f)4 155 116 197 68 99 1610 2


A = event the student took at most 8 hoursB = event the student took at least 7 hours


250)

65


10+ 2

A student is selected at random. The events A, B, and C are defined as follows.

A = event the student took more than 9 hoursB = event the student took less than 6 hoursC = event the student took between 7 and

9 hours inclusive


251)

252) The age distribution of students at a community college is given below. Age (years) Number of students (f)Under 21 289021-24 219025-28 127629-32 65133-36 27437-40 117Over 40 185


A = event the student is at most 28B = event the student is at least 40


252)

66


A student from the community college is selected at random. The events A, B, and C are defined asfollows.

A = event the student is at most 32B = event the student is at least 37C = event the student is between 21 and 24 inclusive


253)



A = event the student is at most 28B = event the student is at least 37

Are the events (not A) and B mutually exclusive?A) Yes B) No

254)

Find the indicated probability.255) A sample space consists of 49 separate events that are equally likely. What is the probability of

each?

A) 0 B) 1 C) 149

D) 49

255)

256) On a multiple choice test, each question has 7 possible answers. If you make a random guess onthe first question, what is the probability that you are correct?

A) 7 B) 1 C) 17

D) 0

256)

67

257) A 12-sided die is rolled. What is the probability of rolling a number less than 11?

A) 112

B) 56

C) 10 D) 1112

257)

258) A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomlyselected from the bag, what is the probability that it is blue?

A) 316

B) 13

C) 16

D) 17

258)

259) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leapyears.

A) 112

B) 131

C) 1365

D) 31365

259)

260) A class consists of 44 women and 14 men. If a student is randomly selected, what is the probabilitythat the student is a woman?

A) 158

B) 227

C) 2229

D) 729

260)

261) In a poll, respondents were asked whether they had ever been in a car accident. 362 respondentsindicated that they had been in a car accident and 475 respondents said that they had not been in acar accident. If one of these respondents is randomly selected, what is the probability of gettingsomeone who has been in a car accident?

A) 0.568 B) 0.762 C) 0.003 D) 0.432

261)

262) The distribution of B.A. degrees conferred by a local college is listed below, by major.

Major FrequencyEnglish 2073Mathematics 2164Chemistry 318Physics 856Liberal Arts 1358Business 1676Engineering 868

9313

What is the probability that a randomly selected degree is in Engineering?A) 0.0932 B) 0.1028 C) 0.0012 D) 868

262)

263) A survey resulted in the sample data in the given table. If one of the survey respondents israndomly selected, find the probability of getting someone who lives in a flat.

Type ofaccommodation Number

House 282Flat 499

Apartment 518Other 410

A) 0.384 B) 499 C) 0.002 D) 0.292

263)

68

Find the indicated probability by using the special addition rule.264) The age distribution of students at a community college is given below.

Age (years) Number of students (f)Under 21 41121-25 41426-30 20031-35 54Over 35 23

1102

A student from the community college is selected at random. Find the probability that the studentis between 26 and 35 inclusive. Round approximations to three decimal places.

A) 0.181 B) 254 C) 0.049 D) 0.230

264)


1103

A student from the community college is selected at random. Find the probability that the studentis at least 31. Round approximations to three decimal places.

A) 0.050 B) 0.070 C) 77 D) 0.930

265)

266) A relative frequency distribution is given below for the size of families in one U.S. city. Size Relative frequency2 0.4303 0.2354 0.1955 0.0956 0.0277+ 0.018

A family is selected at random. Find the probability that the size of the family is less than 5. Roundapproximations to three decimal places.

A) 0.430 B) 0.860 C) 0.095 D) 0.525

266)

69


A family is selected at random. Find the probability that the size of the family is between 2 and 5inclusive. Round approximations to three decimal places.

A) 0.522 B) 0.427 C) 0.949 D) 0.852

267)

268) A percentage distribution is given below for the size of families in one U.S. city. Size Percentage2 50.53 24.04 12.25 7.66 3.87+ 1.9

A family is selected at random. Find the probability that the size of the family is at most 3. Roundapproximations to three decimal places.

A) 0.745 B) 0.240 C) 0.255 D) 0.505

268)


A family is selected at random. Find the probability that the size of the family is at least 5. Roundapproximations to three decimal places.

A) 0.824 B) 0.942 C) 0.176 D) 0.058

269)

70



9313

What is the probability that a randomly selected degree is in English or Mathematics?A) 0.455 B) 0.424 C) 0.517 D) 0.010

270)

271) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an aceor a 9?

A) 213

B) 132

C) 513

D) 10

271)

272) Two 6-sided dice are rolled. What is the probability that the sum of the numbers on the dice is 6 or10?

A) 29

B) 160

C) 49

D) 43

272)

273) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a facecard or a 4?

A) 413

B) 4852

C) 16 D) 213

273)

Find the indicated probability by using the complementation rule.274) The age distribution of students at a community college is given below.

Age (years) Number of students (f)Under 21 41821-24 41125-28 26229-32 14633-36 9437-40 59Over 40 92

1482

A student from the community college is selected at random. Find the probability that the studentis 21 years or over. Give your answer as a decimal rounded to three decimal places.

A) 0.656 B) 0.282 C) 0.277 D) 0.718

274)

71


1482

A student from the community college is selected at random. Find the probability that the studentis under 37 years old. Give your answer as a decimal rounded to three decimal places.

A) 0.895 B) 0.038 C) 0.061 D) 0.105

275)


A family is selected at random. Find the probability that the size of the family is at most 6. Roundapproximations to three decimal places.

A) 0.982 B) 0.027 C) 0.955 D) 0.045

276)


A family is selected at random. Find the probability that the size of the family is at least 3. Roundapproximations to three decimal places.

A) 0.641 B) 0.565 C) 0.359 D) 0.206

277)

72


A family is selected at random. Find the probability that the size of the family is 4 or more. Roundresults to three decimal places.

A) 0.878 B) 0.122 C) 0.324 D) 0.202

278)


A family is selected at random. Find the probability that the size of the family is less than 6. Roundresults to three decimal places.

A) 0.028 B) 0.982 C) 0.046 D) 0.954

279)

280) Based on meteorological records, the probability that it will snow in a certain town on January 1stis 0.159. Find the probability that in a given year it will not snow on January 1st in that town.

A) 1.159 B) 6.289 C) 0.189 D) 0.841

280)

281) The probability that Luis will pass his statistics test is 0.93. Find the probability that he will fail hisstatistics test.

A) 0.07 B) 1.08 C) 0.47 D) 13.29

281)

282) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignoreleap years.

A) 0.093 B) 0.915 C) 0.085 D) 0.917

282)

73



9313

What is the probability that a randomly selected degree is not in Mathematics?A) 0.232 B) 0.303 C) 0.768 D) 0.682

283)

Find the indicated probability by using the general addition rule.284) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either

doubles are rolled or the sum of the dice is 8.

A) 518

B) 14

C) 136

D) 1136

284)

285) For a person selected randomly from a certain population, events A and B are defined as follows.

A = event the person is maleB = event the person is a smoker

For this particular population, it is found that P(A) = 0.50, P(B) = 0.28, and P(A & B) = 0.15. FindP(A or B). Round approximations to two decimal places.

A) 0.48 B) 0.93 C) 0.63 D) 0.78

285)

286) In one city, 50.8% of adults are female, 9.6% of adults are left-handed, and 5.1% are left-handedfemales. For an adult selected at random from the city, let

F = event the person is femaleL = event the person is left-handed.

Find P(F or L). Round approximations to three decimal places.A) 0.553 B) 0.502 C) 0.604 D) 0.700

286)

287) Let A and B be events such that P(A) = 736

, P(B) = 29, and P(A or B) = 29

72.

Determine P(A & B).

A) 5972

B) 512

C) 7162

D) 172

287)

288) Let A and B be events such that P(A) = 17, P(A or B) = 1

2, and P(A and B) = 1

8. Determine P(B).

A) 514

B) 4356

C) 156

D) 2756

288)

74

289) A lottery game has balls numbered 1 through 21. What is the probability of selecting an evennumbered ball or the number 8 ball?

A) 1021

B) 218

C) 10 D) 821

289)

290) A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop onan even number or a multiple of 3?

A) 12 B) 79

C) 13

D) 23

290)

291) If you pick a card at random from a well shuffled deck, what is the probability that you get a facecard or a spade?

A) 122

B) 926

C) 1126

D) 2552

291)

292) Of the 57 people who answered ʺyesʺ to a question, 9 were male. Of the 91 people who answeredʺnoʺ to the question, 15 were male. If one person is selected at random from the group, what is theprobability that the person answered ʺyesʺ or was male?

A) 0.547 B) 0.162 C) 0.486 D) 0.158

292)

293) The manager of a bank recorded the amount of time each customer spent waiting in line duringpeak business hours one Monday. The frequency table below summarizes the results.

Waiting Time (minutes)

Number ofCustomers

0-3 124-7 138-11 1212-15 716-19 520-23 124-27 1

If we randomly select one of the times represented in the table, what is the probability that it is atleast 12 minutes or between 8 and 15 minutes?

A) 0.51 B) 0.647 C) 0.76 D) 0.137

293)

Determine the possible values of the random variable.294) Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four

tosses. What are the possible values of the random variable X?A) 0, 1, 2, 3, 4B) 1, 2, 3, 4C) 1, 2, 3D) HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH,

THTT, TTHH, TTHT, TTTH, TTTT

294)

295) Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of thetwo numbers. What are the possible values of the random variable X?

A) 0, 1, 2, 3, 4, 5 B) 1, 2, 3, 4, 5C) -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 D) 0, 1, 2, 3, 4, 5, 6

295)

75

296) Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. What arethe possible values of the random variable Y?

A) 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20, 24, 30B) 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36C) (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3,

4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1),(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

D) 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36

296)

297) Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote the value ofG - R where G represents the number on the green die and R represents the number on the red die.What are the possible values of the random variable Y?

A) -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 B) 0, 1, 2, 3, 4, 5C) 0, 1, 2, 3, 4, 5, 6 D) -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6

297)

298) For a randomly selected student in a particular high school, let Y denote the number of livinggrandparents of the student. What are the possible values of the random variable Y?

A) 0, 1, 2, 3, 4 B) 4 C) 1, 2, 3, 4 D) 0, 1, 2

298)

299) The following table displays a frequency distribution for the number of siblings for students in onemiddle school. For a randomly selected student in the school, let X denote the number of siblingsof the student. What are the possible values of the random variable X?

Number of siblings 0 1 2 3 4 5 6 7Frequency 189 245 102 42 24 13 5 2

A) Brother, sister B) 189, 245, 102, 42, 24, 13, 5, 2C) 0, 1, 2, 3, 4, 5, 6, 7 D) 7

299)

300) The following frequency distribution analyzes the scores on a math test. For a randomly selectedscore between 40 and 99, let Y denote the number of students with that score on the test. What arethe possible values of the random variable Y?

A) 2, 4, 6, 5 B) 32 C) 2, 4, 6, 15, 5 D) 2, 4, 6, 15

300)

76

301) The following frequency distribution lists the annual household incomes (in thousands of dollars)of one neighborhood in a large city. For a randomly selected income between $200,000 and$700,000, let Y denote the number of households with that income. What are the possible values ofthe random variable Y?

Incomes Frequency200-300 68301-400 60401-500 72501-600 79601-700 20A) 20 B) 68, 60, 72, 79 , 20C) 68, 60, 72, 79 D) 299

301)

Use random-variable notation to represent the event.302) Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four

tosses. Use random-variable notation to represent the event that the total number of tails is three.A) {X = 3} B) HTTT, THTT, TTHT, TTTHC) {X ≥ 3} D) P{X = 3}

302)

303) Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of thetwo numbers. Use random-variable notation to represent the event that the absolute value of thedifference of the two numbers is 2.

A) {X = 2}B) {(1, 3), (2, 4), (3, 5), (4, 6), (3, 1), (4, 2), (5, 3), (6, 4)}C) P{X = 2}D) X = 2

303)

304) Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. Userandom-variable notation to represent the event that the product of the two numbers is greaterthan 4.

A) {Y > 4} B) {XY > 4} C) {5, 6} D) P{Y > 4}

304)

305) Suppose that two balanced dice are rolled. Let Y denote the sum of the two numbers. Userandom-variable notation to represent the event that the sum of the two numbers is at least 11.

A) {X+Y ≥ 11} B) {Y > 11}C) {Y ≥ 11} D) (5, 6), (6, 5), (6,6)

305)

306) Suppose that two balanced dice are rolled. Let Y denote the sum of the two numbers. Userandom-variable notation to represent the event that the sum of the two numbers is at least 3 butless than 5.

A) {3 < Y < 5} B) {3 ≤ Y < 5}C) {3 ≤ X+Y < 5} D) (1, 2), (2, 1), (1, 3), (3, 1), (2, 2)

306)

307) Suppose that two balanced dice are rolled. Let X denote the sum of the two numbers. Userandom-variable notation to represent the event that the sum of the two numbers is less than 4.

A) (1, 1), (1, 2), (2, 1) B) {X ≤ 4}C) {X+Y < 4} D) {X < 4}

307)

77

308) For a randomly selected student in a particular high school, let Y denote the number of livinggrandparents of the student. Use random-variable notation to represent the event that the studentobtained has exactly three living grandparents.

A) {Y ≥ 3} B) {Y = 3} C) {Y < 3} D) P{Y = 3}

308)

309) For a randomly selected student in a particular high school, let Y denote the number of livinggrandparents of the student. Use random-variable notation to represent the event that the studentobtained has at least two living grandparents.

A) {Y ≥ 2} B) P{Y ≥ 2} C) {Y > 2} D) {2, 3, 4}

309)

310) The following table displays a frequency distribution for the number of siblings for students in onemiddle school. For a randomly selected student in the school, let X denote the number of siblingsof the student.


Use random-variable notation to represent the event that the student obtained has fewer than twosiblings.

A) {X ≤ 2} B) {0, 1} C) {X < 2} D) P{X < 2}

310)

311) The following table displays a frequency distribution for the number of siblings for students in onemiddle school. For a randomly selected student in the school, let Y denote the number of siblingsof the student.


Use random-variable notation to represent the event that the student obtained has at least two butfewer than six siblings.

A) {2 ≤ Y < 6} B) {2 < Y < 6} C) {2 ≤ Y ≤ 6} D) {2, 3, 4, 5}

311)

Obtain the probability distribution of the random variable.312) When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below:

HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTTTHHH THHT THTH THTTTTHH TTHT TTTH TTTT

Let X denote the total number of tails obtained in the four tosses. Find the probability distributionof the random variable X. Leave your probabilities in fraction form.

A)x P(X = x)0 1/161 3/162 1/23 3/164 1/16

B)x P(X = x)1 1/42 7/163 1/44 1/16

C)x P(X = x)0 1/161 1/82 3/83 1/84 1/16

D)x P(X = x)0 1/161 1/42 3/83 1/44 1/16

312)

78

313) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Let X denote the absolute value of the difference of the two numbers. Find the probabilitydistribution of X. Give the probabilities as decimals rounded to three decimal places.

A)x P(X = x)0 0.1671 0.2782 0.2223 0.1674 0.1115 0.056

B)x P(X = x)1 0.2782 0.2223 0.1674 0.1115 0.056

C)x P(X = x)0 0.1671 0.1672 0.1673 0.1674 0.1675 0.167

D)x P(X = x)0 0.1671 0.2512 0.2223 0.1674 0.1115 0.0566 0.027

313)


(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Let X denote the smaller of the two numbers. If both dice come up the same number, then X equalsthat common value. Find the probability distribution of X. Leave your probabilities in fractionform.

A)x P(X = x)1 11/362 1/43 7/364 5/365 1/126 1/36

B)x P(X = x)1 5/182 2/93 1/64 1/95 1/186 0

C)x P(X = x)1 1/62 1/63 1/64 1/65 1/66 1/6

D)x P(X = x)1 5/182 1/43 7/364 5/365 1/96 1/36

314)

79


(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Let X denote the product of the two numbers. Find the probability distribution of X. Leave yourprobabilities in fraction form.

A)x P(X = x)1 1/362 1/183 1/184 1/125 1/186 1/98 1/189 1/3610 1/18

x P(X = x)12 1/915 1/1816 1/3618 1/1820 1/1824 1/1825 1/3630 1/1836 1/36

B)

x P(X = x)2 1/183 1/184 1/125 1/186 1/98 1/18

x P(X = x)10 1/1212 1/915 1/1218 1/1220 1/1224 1/1230 1/18

C)x P(X = x)1 1/182 1/183 1/184 1/185 1/186 1/188 1/189 1/1810 1/18

x P(X = x)12 1/1815 1/1816 1/1818 1/1820 1/1824 1/1825 1/1830 1/1836 1/18

D)

x P(X = x)2 1/363 1/184 1/125 1/96 5/36

x P(X = x)7 1/68 5/369 1/910 1/1211 1/1812 1/36

315)

80

316) The following table displays a frequency distribution for the number of living grandparents forstudents at a high school. For a randomly selected student in the school, let X denote the numberof living grandparents of the student. Obtain the probability distribution of X.

Number of living grandparents 0 1 2 3 4Frequency 37 83 151 206 140

A)Grandparents

xProbability

P(X = x)0 0.21 0.22 0.23 0.24 0.2

B)Grandparents

xProbability

P(X = x)1 0.1432 0.2603 0.3554 0.241

C)Grandparents

xProbability

P(X = x)0 0.0601 0.1352 0.2453 0.3344 0.227

D)Grandparents

xProbability

P(X = x)0 0.0681 0.1512 0.2453 0.3184 0.219

316)

317) The following table displays a frequency distribution for the number of siblings for students at onemiddle school. For a randomly selected student in the school, let X denote the number of siblingsof the student. Obtain the probability distribution of X.


A)Siblings

xProbability

P(X = x)1 0.5202 0.2703 0.1264 0.0495 0.0176 0.0137 0.004

B)Siblings

xProbability

P(X = x)0 0.3141 0.3502 0.2013 0.0774 0.0355 0.0126 0.0097 0.003

C)Siblings

xProbability

P(X = x)0 0.1251 0.1252 0.1253 0.1254 0.1255 0.1256 0.1257 0.125

D)Siblings

xProbability

P(X = x)0 0.2991 0.3652 0.1893 0.0894 0.0355 0.0126 0.0097 0.003

317)

81

318) The following frequency table contains data on home sale prices in the city of Summerhill for themonth of June. For a randomly selected sale price between $80,000 and $265,900 let X denote thenumber of homes that sold for that price. Find the probability distribution of X.

Sale Price (in thousands) Frequency (No. of homes sold)

80.0 - 110.9111.0 - 141.9142.0 - 172.9173.0 - 203.9204.0 - 234.9235.0 - 265.9

2571031

A)Sale Price (in thousands) Probability

(P(X = x)80.0 - 110.9111.0 - 141.9142.0 - 172.9173.0 - 203.9204.0 - 234.9235.0 - 265.9

0.0710.1970.2500.3570.1070.036

B)Sale Price (in thousands) Probability

(P(X = x)80.0 - 110.9111.0 - 141.9142.0 - 172.9173.0 - 203.9204.0 - 234.9235.0 - 265.9

0.0710.1790.2500.3570.1070.360

C)Sale Price (in thousands) Probability

(P(X = x)80.0 - 110.9111.0 - 141.9142.0 - 172.9173.0 - 203.9204.0 - 234.9235.0 - 265.9

0.0710.1790.2500.3570.1070.036

D)Sale Price (in thousands) Probability

(P(X = x)80.0 - 110.9111.0 - 141.9142.0 - 172.9173.0 - 203.9204.0 - 234.9235.0 - 265.9

0.0710.1790.0250.3570.1070.036

318)

82

Construct the requested histogram.319) If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H) and tails (T). Suppose

the random variable X represents the number of heads in a sequence. Construct the probabilitydistribution for X.

A) B)

C) D)

319)

83

320) Each person from a group of recently graduated math majors revealed the number of job offersthat he or she had received prior to graduation. The compiled data are represented in the table.Construct the probability histogram for the number of job offers received by a graduate randomlyselected from this group.

Number of offers 0 1 2 3 4Frequency 4 10 25 5 6

A) B)

C) D)

320)

Find the specified probability.321) A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students

waiting to see the professor is a random variable, X, with the distribution shown in the table.

x 0 1 2 3 4 5P(X = x) 0.05 0.10 0.40 0.25 0.15 0.05

The professor gives each student 10 minutes. Determine the probability that a student arriving justafter 9:00 am will have to wait no longer than 20 minutes to see the professor.

A) 0.80 B) 0.55 C) 0.40 D) 0.15

321)

322) A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of studentswaiting to see the professor is a random variable, X, with the distribution shown in the table.

x 0 1 2 3 4 5P(X = x) 0.05 0.10 0.40 0.25 0.15 0.05

The professor gives each student 10 minutes. Determine the probability that a student arriving justafter 9:00 am will have to wait at least 30 minutes to see the professor.

A) 0.45 B) 0.25 C) 0.15 D) 0.85

322)

84

323) The number of loaves of rye bread left on the shelf of a local bakery at closing (denoted by therandom variable X) varies from day to day. Past records show that the probability distribution of Xis as shown in the following table. Find the probability that there will be at least three loaves leftover at the end of any given day. x 0 1 2 3 4 5 6 P(X = x) 0.20 0.25 0.20 0.15 0.10 0.08 0.02

A) 0.20 B) 0.15 C) 0.65 D) 0.35

323)

324) There are only 8 chairs in our whole house. Whenever there is a party some people have no whereto sit. The number of people at our parties (call it the random variable X) changes with each party.Past records show that the probability distribution of X is as shown in the following table. Find theprobability that everyone will have a place to sit at our next party. x 5 6 7 8 9 10 >10 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

A) 0.55 B) 0.15 C) 0.05 D) 0.45

324)

325) Use the special addition rule and the following probability distribution to determine P(X ≥ 8). x 5 6 7 8 9 10 11 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

A) 0.30 B) 0.15 C) 0.45 D) 0.70

325)

326) Use the special addition rule and the following probability distribution to determine P(X = 6). x 5 6 7 8 9 10 11 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

A) 0.10 B) 0.95 C) 0.05 D) 0.90

326)

327) Use the special addition rule and the following probability distribution to determine P(6 < X ≤ 8). x 5 6 7 8 9 10 11 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

A) 1.00 B) 0.45 C) 0.35 D) 0.40

327)

Calculate the specified probability328) Suppose that W is a random variable. Given that P(W ≤ 3) = 0.425, find P(W > 3).

A) 0.425 B) 3 C) 0 D) 0.575328)

329) Suppose that D is a random variable. Given that P(D > 1.8) = 0.65, find P(D ≤ 1.8).A) 0 B) 0.35 C) 0.65 D) 0.175

329)

330) Suppose that K is a random variable. Given that P(-3.65 ≤ K ≤ 3.65) = 0.125, and that P(K < -3.65) =P(K > 3.65), find P(K > 3.65).

A) 0.4375 B) 0.125 C) 0.875 D) 1.825

330)

331) Suppose that T is a random variable. Given that P(2.55 ≤ T ≤ 2.55) = 0.8, and that P(K < 2.55) = P(K> 2.55), find P(K < -2.55).

A) 0.1 B) 0.8 C) 1.275 D) 0.2

331)

332) Suppose that A is a random variable. Also suppose that P(T > a) = P(T < -a) = x, and that P(0 < T ≤a ) = y. Find P(-a ≤ T ≤ 0) in terms of x and y.

A) 1 - y B) y C) 1 - (2x - y) D) 1 - 2x - y

332)

85

Find the mean of the random variable.333) The random variable X is the number of houses sold by a realtor in a single month at the

Sendsomʹs Real Estate office. Its probability distribution is given in the table.x P(X = x)0 0.241 0.012 0.123 0.164 0.015 0.146 0.117 0.21A) 3.35 B) 3.50 C) 3.40 D) 3.60

333)

334) The random variable X is the number of golf balls ordered by customers at a pro shop. Itsprobability distribution is given in the table.

x 3 6 9 12 15P(X = x) 0.14 0.33 0.36 0.07 0.10A) 9 B) 9.54 C) 7.98 D) 5.31

334)

335) The random variable X is the number of people who have a college degree in a randomly selectedgroup of four adults from a particular town. Its probability distribution is given in the table. x P(X = x)0 0.40961 0.40962 0.15363 0.02564 0.0016A) 2.00 B) 1.21 C) 0.80 D) 0.70

335)

336) The random variable X is the number that shows up when a loaded die is rolled. Its probabilitydistribution is given in the table. x P(X = x)1 0.112 0.113 0.114 0.125 0.136 0.42A) 3.50 B) 4.18 C) 4.31 D) 0.17

336)

337) The random variable X is the number of siblings of a student selected at random from a particularsecondary school. Its probability distribution is given in the table.

x 0 1 2 3 4 5

P(X = x) 1348

724

16 748

112

124

A) 1.5 B) 1.875 C) 1.604 D) 2.5

337)

86

Find the standard deviation of the random variable.338) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a

given day are 0.51, 0.36, 0.11, and 0.02, respectively. Find the standard deviation for theprobability distribution.

A) 1.04 B) 0.76 C) 0.99 D) 0.57

338)

339) The random variable X is the number of houses sold by a realtor in a single month at theSendsomʹs Real Estate office. Its probability distribution is given in the table. Houses Sold (x) Probability P(x)

0 0.241 0.012 0.123 0.164 0.015 0.146 0.117 0.21

A) 4.45 B) 2.62 C) 2.25 D) 6.86

339)

340) The random variable X is the number of people who have a college degree in a randomly selectedgroup of four adults from a particular town. Its probability distribution is given in the table. x P(X = x)0 0.02561 0.15362 0.34563 0.34564 0.1296A) 2.59 B) 0.96 C) 0.98 D) 1.12

340)

341) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are0.5997, 0.3271, 0.0669, 0.0061, and 0.0002, respectively.

A) 0.59 B) 0.65 C) 0.42 D) 0.81

341)

342) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in agiven day are 0.51, 0.40, 0.07, and 0.02, respectively. Find the standard deviation for theprobability distribution.

A) 0.50 B) 0.71 C) 0.93 D) 1.00

342)

343) The random variable X is the number of siblings of a student selected at random from a particularsecondary school. Its probability distribution is given in the table.

x 0 1 2 3 4 5

P(X = x) 1348

516

524

18 124

124

A) 1.606 B) 0.964 C) 1.927 D) 1.338

343)

The probability distribution of a random variable is given along with its mean and standard deviation. Draw aprobability histogram for the random variable; locate the mean and show one, two, and three standard deviationintervals.

87

344) x 4 5 6 7 8P(X = x) 0.1 0.3 0.45 0.1 0.05

μ = 5.7, σ = 0.95A)

B)

C)

344)

345) The random variable X is the number of tails when four coins are flipped. Its probabilitydistribution is as follows.

x 0 1 2 3 4

P(X = x) 116

14 38 14 116

μ = 2, σ = 1

345)

88

A)

B)

C)

Find the expected value of the random variable.346) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning

ticket is to be $500. What is your expected value?A) -$1.00 B) -$0.40 C) $0.00 D) -$0.50

346)

347) In a game, you have a 1/26 probability of winning $57 and a 25/26 probability of losing $4. What isyour expected value?

A) -$3.85 B) $2.19 C) $6.04 D) -$1.65

347)

89

348) A contractor is considering a sale that promises a profit of $27,000 with a probability of 0.7 or a loss(due to bad weather, strikes, and such) of $17,000 with a probability of 0.3. What is the expectedprofit?

A) $30,800 B) $18,900 C) $13,800 D) $10,000

348)

349) Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 forrolling a 2 or a 3, nothing otherwise. What is your expected value?

A) $2.00 B) -$0.67 C) $4.00 D) -$2.00

349)

350) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winningticket is to be $500. What is your expected value?

A) -$0.50 B) -$1.00 C) $0.00 D) -$0.40

350)

351) Sue Anne owns a medium-sized business. Use the probability distribution below, where Xdescribes the number of employees who call in sick on a given day.

Number of Employees Sick 0 1 2 3 4 P(X = x) 0.05 0.45 0.25 0.15 0.1

What is the expected value of the number of employees calling in sick on any given day?A) 1.85 B) 2.00 C) 1.80 D) 1.00

351)

352) The probability distribution below describes the number of thunderstorms that a certain town mayexperience during the month of August. Let X represent the number of thunderstorms in August.

Number of storms 0 1 2 3P(X = x) 0.1 0.3 0.5 0.1

What is the expected value of thunderstorms for the town each August?A) 1.5 B) 2.0 C) 1.6 D) 1.7

352)

90

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