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MAT-225. Introductory StatisticsFinal Exam. Spring 2010

Name _________________________________________Date____________________________

1. According to the Uniform Crime Report, 2007, 66.9% of murders arecommitted with a firearm.

a) In a random sample of 10 murders, find the probability that exactly 8 willbe committed with a firearm.

b) In a random sample of 10 murders, find the probability that fewer than 6will be committed with a firearm.

c) In a random sample of 10 murders, find the probability that at least 5 will

be committed with a firearm.

d) In a random sample of 200 murders, what is the expected number or meanthat would be committed with a firearm?

e) In a random sample of 200 murders, what is the standard deviation?

Final Exam Spring 2010 1 Mat-225: Introductory Statistics

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2. Use the standard normal distribution table.

a) Find the area under the standard normal distribution to the left of z =1.34

b) Find the area under the standard normal distribution to the right of z =0.93

c) Find the area under the standard normal distribution that lies between z= -2.03 and z = 1.55

d) Find the z-score such that the area under the standard normal curve to theleft is 0.8438.

Final Exam Spring 2010 2 Mat-225: Introductory Statistics

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e) Find the Z-scores that separate the middle 94% of the distribution from thearea in the tails of the standard normal distribution.

3. The magnitude of earthquakes since 1900 that measure 0.1 or higher onthe Richter scale in California is approximately normally distributed with amean = 6.2 and a standard deviation

= 0.5, according to data obtainedfrom the U.S. Geological Service.

a) What percent of the earthquakes has a magnitude above 6.8?

b) What percent of the earthquakes has a magnitude below 5?

c) What percent of the earthquakes has a magnitude above between 5.2 and6.5?

d) What percent of the earthquakes has a magnitude below 6?

Final Exam Spring 2010 3 Mat-225: Introductory Statistics

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e) What percent of the earthquakes has a magnitude above 9? Is thatunusual?

4. Scores on the Stanford-Binet Intelligence Test (IQ Test) are normally

distributed with mean = 100 and a standard deviation

= 16.

a) What is the probability that a randomly selected individual has an IQ scorebellow 110?

b) What is the probability that a random sample of 25 individuals has a meanIQ score bellow 110?

c) What is the probability that a random sample of 55 individuals has a meanIQ score bellow 110?

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d) What effect does increasing the sample size have on the probability?

5. A simple random sample of size n is drawn from a population that is knownto be normally distributed. The sample mean,X , is determine to be 104.3and the sample standard deviation, s, is determined to be 15.9.

a) Construct the 90% confidence interval about the population mean if thesample size, n, is 15.

b) Construct the 90% confidence interval about the population mean if thesample size, n, is 25. How does increasing the sample size affect the width ofthe interval?

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c) Construct the 95% confidence interval about the population mean if the

sample size, n, is 15. Compare the results to those obtained in part (a). Howdoes increasing the level of confidence affect the confidence interval?

6. In 2000, as reported by ACT research service, the mean ACT Math score was = 20.7 Mrs.

Teresa Gibson wants to estimate the mean ACT Math score of students in High School district

204. She obtains a simple random sample of 20 students who took the ACT in 2000, looks up the

ACT Math scores, and obtains the results shown . Assume that the

=5.

24 23 16 26 25

22 18 25 26 17

28 27 23 21 23

20 25 21 19 30

a). Use the data to compute a point estimate for the population mean ACT Math score of High

School District 204.

b) Because the sample size is small, we must verify that ACT scores are normally distributed

and that the sample does not contain any outliers. Construct a normal probability plot or

the boxplot. Are the conditions for constructing a z-interval satisfied?

c) Construct a 92% confidence interval for the mean ACT Math score for all students inDistrict 204 who took the exam. Interpret this interval.

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d) Do Mrs. Gibsons students appear to have a mean ACT Math score different from that of the

general population?

7. A sociologist claims that the mean age at which women marry in Memphis, Tennessee, is

greater than the mean age of 25.0 throughout the U.S. Based upon a random sample of 20 recently

married certificates, she obtains the ages shown in the table below.

40 23 30 24 31 29 28 24 35 34

24 21 46 29 31 29 29 21 33 39

a) Construct a boxplot and a normal probability plot to verify that the marriage is normally

distributed and the data set does not contain any outliers. Note: use the graphing calculator to get

the graphs and then draw a sketch here or transfer the graph to the computer and print.

b) Test the hypothesis, assuming that = 6.2 at the = 0.05 level of significance.

Final Exam Spring 2010 7 Mat-225: Introductory Statistics