georgia online formative assessment resource (gofar) g9...

G9-C-STA+PRO-Q2-39

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Georgia Online Formative Assessment Resource (GOFAR)

Copyright © 2015by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 34 )

1. A theater on a college campus has 618 audience seats on two levels. The diagram shows the seating chart and the numberof seats in the left, center, and right sections of each level.

All seats are filled for a charity event, and a raffle is held to award prizes. The tickets from the audience are placed into alarge bin and mixed well.

Part AOne ticket is selected at random from the 618 tickets in the bin. If the selected ticket is known to be a main floor ticket, whatis the probability that it is from the left section of the main floor? Show your work and explain your answer.

Part BOne ticket is selected at random from the 618 tickets in the bin. If the selected ticket is known to be a center section ticket,what is the probability that it is from the balcony? Show your work and explain your answer.

Part COne ticket is selected at random from the 618 tickets in the bin. If it is known that the selected ticket is NOT from the leftsection of the theater, what is the probability that it is from the right section? Show your work and explain your answer.

Be sure to complete ALL parts of the task.Write your answer and show your work on the paper provided.

Do NOT type your answer in the text box below.



2. The transportation department of a school district wanted to estimate the number of students who live acertain distance from the high school. They surveyed 100 randomly selected students out of the 562students at the school, asking how many miles they live from the school. The mean distance of the samplewas 3.7 miles with a standard deviation of 1.2 miles. The data had a normal distribution.

Part ABased on the sample, approximately how many students in the school live 2.5 miles or more from the highschool? Explain how you determined your answer.

Part BWhat is the median distance that students live from the school? Explain how you determined your answer.

Part CApproximate the maximum and minimum distances from school between which at least 99% of thestudents live. Explain how you determined your answer.



3. Skyler and Jordan plan to use two fair number cubes with faces numbered 1 through 6 in an experiment. They will eachroll the number cubes 100 times, recording the sum of each roll. Before rolling the number cubes, they each madepredictions about what the frequency of each sum would be.



Part AWhose prediction more closely resembles the expected results of an actual experiment of 100 numbercube rolls? Show your work.

If the results of the experiment match the prediction that was not closer to the expected results, wouldyou question your model? Explain your answer.

Part BCompare the mean value of Skyler’s predictions to the mean value of Jordan’s predictions. Show your workand explain your answer.



4. The two-way frequency table shows data from a survey of students enrolled in science classes at Einstein College.



Part ABased on the model, how much more likely is it that a student chosen at random would be enrolled inGeneral Science or Physics than Chemistry? Show your work or explain your answer.

Part BUsing the data from the model, estimate the probability that a randomly selected student would be enrolledin Biology given that the student is in the 9th grade. Show your work or explain your answer.

Part CAccording to the model, are the probability of a student enrolled in Chemistry and the probability of astudent enrolled in 12th grade independent of each other? Justify your answer by showing or explaining yourwork.



5. The two-way frequency table shows information from a random sample of students about participation in school-sponsoredactivities and enrollment in foreign language classes.



Part ACopy and complete the two-way frequency table showing the data in the table and its marginal frequencies.Explain how you found your answers. Create a table showing the conditional probabilities by participation inschool-sponsored activities and another table showing the conditional probabilities by enrollment in foreignlanguage classes. Show your work and round the probabilities to the nearest hundredth. What trends areshown by the data?

Part BThere are 426 students in the school. The conditional probability that a female student participates in aschool-sponsored activity is 0.80, and the conditional probability that a male student is enrolled in amathematics class is 0.80. Are the two probabilities independent of each other? Explain your answer.



6. The total number of full-time and part-time employees at a store is 50. Each employee works either themorning shift or the afternoon shift. More information about the employees is given below.

●15 employees are part-time

●28 employees are males



●30 employees work the morning shift

●6 male employees work part-time

●12 male employees work the morning shiftThe names of each of the 50 employees are written on separate cards. The cards are shuffled and placed into a container.

Part AIf one card is selected at random from all 50 cards in the container, what is the probability that the employee is part-time ormale? Show your work and explain your answer.

Part BIf one card is selected at random from all 50 cards in the container, what is the probability that the employee is male orworks the afternoon shift? Show your work and explain your answer.

Part CIf one card is selected at random from all 50 cards in the container, what is the probability that the employee is a female whodoes not work the morning shift? Show your work and explain your answer.



7. A pharmaceutical lab conducts two studies. The researchers want to determine if their allergy medicationstops eyes from itching.

In the first study, the researchers interview people who have complained of itchy eyes. The participants aredivided into two groups, those using the allergy medication and those not using it.

In the second study, the researchers recruit people who suffer from allergies that cause itchy eyes.Participants are assigned to Group A or Group B at random and do not know which group they are in.Group A receives the allergy medication and Group B receives a placebo. The researchers record thereduction of eye itchiness in each group after one treatment.

Part AIs the data-gathering process described in the first study an observational study, an experiment, or asample survey? What is an advantage to this data-gathering process? Explain your answer.

Part BIs the data-gathering process described in the second study an observational study, an experiment, or asample survey? Why is random selection important in this data-gathering process? Explain your answer.

Part C



Group A has 40 members, and Group B has 25 members. The table shows the results of the second study.

Does the medication being tested appear to reduce the occurrence of itchy eyes? Justify your conclusion.



8. In an experiment, 100 randomly selected strings of lights from Brand A and 100 randomly selectedstrings of lights from Brand B were left on for two months. After two months, 84% of Brand A strings werestill lit and 72% of Brand B strings were still lit. The sample difference between the proportions of Brand Astrings still lit compared to Brand B strings still lit is 0.12. The standard error of the differences inproportions is

Part AConsidering the margin of error, explain if a difference of 0 is a reasonable result.

Part BIn the context of this problem, what does a difference of 0 mean?

Part CIs it reasonable to conclude that there is a true difference in the quality of Brand A light strings and BrandB light strings? Explain your reasoning in terms of percents.





9. Two competing airlines offer commuter flights from Los Angeles to Catalina Island. The table represents one year of datafor flights at both airlines.

Part ACalculate the on-time rate for all flights for both airlines over the past year.

Part BCalculate the on-time rate for Airline A. Calculate the on-time rate for Airline B. Show your work.

Compare the two airlines. Which airline would you choose to fly to Catalina if your main concern is being ontime? Explain your answer.

Part CWhat proportion of delayed flights was Airline A responsible for? What proportion of on-time flights wasAirline B responsible for? Show your work.

Part DThe on-time rate for flights at Airline B has been charted for prior years.

Identify the trend in the data. Based on the on-time rate that you calculated for this year, predict what will happen to the on-time rate in upcoming years.





10. One hundred high school students were asked which type of music, limited to rock and country, they like to listen to. Theresults of the survey will be displayed in the two-way table shown.

The survey showed that 50 students like both rock music and country music, 31 do not like either rock orcountry music, 12 like rock music but do not like country music and 7 like country music but do not likerock music.

Part ACopy the table onto your paper and record the data given in the table. Then complete the table by filling inthe marginal frequencies.

Part BIs there evidence of a positive association between liking rock music and liking country music? Explain youranswer.

Part CSuppose you interview another student from the population represented by this sample, and that studentdoes not like country music. Based on the sample, what is the probability that this student does like rockmusic? Explain your answer.



11. The director of a community recreation center would like to increase the number of teens who participate in summerprograms. She creates a questionnaire to gather data about the types of programs that teens in the community like. Thecommunity has approximately 2,000 teens, but the director’s funds are limited. She has decided to give the questionnaire to50 teens and then draw conclusions from the results.



Part AIs the data-gathering process described part of an observational study, an experiment, or a sample survey? Explain youranswer.

Part BSuppose that the director gives the 50 questionnaires to the first 50 teenage boys who show up for the boys’ soccertournament. Is her selection of teens a good one statistically? Explain your answer.

Part CSuppose that the director is given permission to distribute the questionnaires to students at the community’s only high schoolsince almost all of the local teens attend that school. She selects 50 students at random from the list of all students andgives them the questionnaire. Is her selection of teens a good one statistically? Explain your answer.

Part DIf the director uses the method of data-gathering in Part C, describe a method she could use to ensure that the students areselected at random. Why is random selection important in this process?



12. The dot plot shows Kim’s quiz scores for last semester. The maximum score on each quiz is 10.

The table shows Kim’s quiz scores for this semester.



Part ACreate a dot plot for Kim’s quiz scores for this semester.

Part BWhat is the difference between the means of the two data sets? Show your work.

Part CKim takes two more quizzes this semester. The mean for this semester’s quiz scores decreases by 1 fromwhat is shown in the table. What could be Kim’s scores on these two quizzes? Show your work or explainyour answer.



13. The two-way frequency table shows the adoption data for an animal shelter for the first five months of ayear.

Part AWhat is the difference between the interquartile ranges of the number of cats adopted and the number ofdogs adopted during the first five months? Show your work or explain your answer.

Part BCreate a conditional relative frequency table for this data. Explain the values you used in your table.





14. The table shows the amounts Anita earned for babysitting.

Part AA linear model for the data is What do the slope and y -intercept of the linear modelrepresent in the context of the given data?

Part BAnalyze the residuals for the data shown in the table. Show your work and explain your answer.



15. Kei is reading a book for a book report. He records the total number of pages he has read at the end ofeach day. The line of best fit for Kei’s reading data is where y represents the total number ofpages Kei has read in terms of x , the number of days Kei has read the book.

Part AWhat are the slope and y -intercept of the given function? Explain the meaning of the slope and y -intercept within the context of Kei’s reading data.

Part BThe residual for each x -value is shown in the table.



Using the residuals in the given table, make another table that shows the y- values that are paired with thex- values.

Sketch a coordinate plane and create a scatter plot using the data you generated. Then graph the line ofbest fit on the same coordinate plane. Remember to title your graph and label the axes.



16. Jeff collected information from 100 cities in the United States. He plotted the average monthlytemperature for September ( x ) and the total number of inches of rainfall in September ( y). Using hiscalculator, Jeff determined the equation for a line of best fit. The correlation coefficient for his data is

Part AWhat information does the correlation coefficient give about the strength of the linear relationship betweentemperature and rainfall? Explain your answer.

Part BHow useful is Jeff’s line of best fit for predicting rainfall from temperature? Explain your answer.

Part CJeff switched the x and y values for all of the ordered pairs of his original data and plotted the results. Howdoes the r of this new data set compare with his original r ? Explain how you know.

Part DAfter Jeff switched the x and y values for the original data and plotted the results, is the line of best fit ofthis new data set the same as his original line of best fit? Explain how you know.

Be sure to complete ALL parts of the task.



Write your answer and show your work on the paper provided.Do NOT type your answer in the text box below.

17. A car dealer summarizes his business by recording the number of customers who purchased or leasedcars. He also records the size of the car (small, midsize, and full-size). The table shows his summary forone week.

Part ARegardless of whether a customer purchased or leased a car, which size was most preferred? Justify youranswer using the information in the table.

Part BOf the people who purchased a car, what trend (in terms of car size) appears to be true for that week?Explain your reasoning.

Part CWhat association do you see between the type of sale (purchased or leased) and the size of the car? Justifyyour answer using the information in the table.





18. Several students completed a paper-and-pencil maze multiple times in an experiment. Their times, inseconds ( y ), were plotted against the number of previous attempts they had made ( x ) in a scatter plotas shown.

A linear model that describes the data is given by the equation

Part AInterpret the slope of the line in terms of the context.

Part BDetermine the y -intercept of the line. Explain what the y -intercept represents in terms of the context.

Part CDetermine the x -intercept of the line. What is the significance of the x -intercept in terms of the context?Explain your answer.





19. All of a city’s schools participated in a food-collection drive to stock the community food pantry. Eachschool reported the number of pounds of food collected. The histogram shows the results of the communityfood drive.

Part AIn which interval is the median number of pounds collected by the schools located? Explain your answer.

Part BThe same schools participated in the food-collection drive the previous year. The box plot gives the resultsfor the previous year.

Estimate the difference, in pounds, between the medians of the two sets of data. Could the two medians beequal? Justify your answer.

Part CWith the information you have from the box plot, create a histogram that could represent the data from theprevious year. Use the same weight intervals that are used in the given histogram. Remember to title thenew histogram and label your axes.

Explain your strategy for determining the frequencies you used for the weight intervals in your histogram.





20. Jelena is considering buying a used car from two different dealerships. The list shows the prices of thecars Jelena is considering buying from Dealership A.

The box plot displays the prices of the 7 cars Jelena is considering buying from Dealership B.

Part ADraw a box plot to represent the prices of the cars Jelena is considering buying from Dealership A.

Part BWhat is the difference in the interquartile ranges of the two data sets? Show your work.

Part CFor which dealership is the mean of the prices of the cars that Jelena is considering buying greater? Explainyour answer.

Part DWhat is the median car price for each dealership? Compare the medians and means for each dealership.Which best represents the prices at each dealership, the mean or the median? Explain your answer.



21. The table shows the number of bacteria in a culture at different times during an experiment.



Part AWhat was the number of bacteria at the beginning of the experiment? Show your work or explain youranswer.

Part BWrite an exponential equation that fits the data for n , the number of bacteria, in terms of h , the numberof hours since the experiment began.

Part CUse your equation from Part B to find the number of bacteria 4 hours after the experiment began. Showyour work.

Part DSketch a graph of the equation that represents the data for the first 4 hours of the experiment. Label thescales for both axes. Include an appropriate title for the graph and for each axis.



22. The scatter plot shows Grace’s distance, in miles, from her destination at the end of each hour duringher car trip.



Part AWrite a linear function that fits the data shown in the scatter plot. Explain how you determined yourfunction.

Part BIdentify and interpret the slope, x -intercept, and y -intercept of the linear function in the context of thesituation.

Part CDefine the domain of the function that best fits this situation. Explain your answer.



23. Incoming freshmen at a community college can take a placement test to determine if they are eligiblefor a college Calculus class. A student needs to score 50 or more points to enroll in Calculus I. Studentsscoring less than 50 points must enroll in a Pre-Calculus course first. The box plots show the data collectedfrom the scores of 24 females and 24 males who took a recent placement test.



Part AIs the interquartile range (IQR) for females greater, less, or equal to that of males? Explain your answer.

Part BEstimate the median score for females and the median score for males. Justify your estimates.

Part CUse the shape of the distribution to estimate the mean score for females. Explain your answer.

Part DUse the shape of the distribution to estimate the mean score for males. Explain your answer.

Part EOne of the 48 students selected at random is eligible to enroll in Calculus I based on the student’s score.What is the probability that the randomly-selected student is a male? Explain your reasoning.



24. A distribution of the weekly earnings, in dollars, of students in a statistics class is shown in thehistogram.

Part AIn which interval is the median of this distribution located? Explain your answer.

Part BIf the data set is graphed as a box-and-whisker plot, describe how the upper and lower whiskers would



compare with each other.

Part COne of the students made a dot plot of this data set. Explain what information a dot plot would provide thatis not provided by the histogram.

Part DOne of the students was absent the day the data was collected, and his weekly salary of $200 is added tothe data set. Explain what effect, if any, this new data point has on the median.



25. Garret sells laptop and desktop computers. He asks his customers what the computer will be primarilyused for-school, home, or work. The table shows Garret's yearly summary giving the proportion of eachtype of computer he sold and its primary use.

Part AWhat proportion of Garret's sales are computers primarily used for school or work? Show your work andexplain your answer.

Part BConsider the following two situations:

A customer buys a computer from Garret for work.

A customer buys a desktop computer from Garret.Based on the data in the table, which of the two situations is most likely to occur? Show your work andexplain your answer.

Part CIf Garret randomly selects a customer from those who purchased a desktop computer, what is theprobability the customer uses the computer primarily for work? Show your work and explain your answer.

Part DIf Garret randomly selects a customer from those who purchased a computer primarily for school, what isthe probability the customer bought a laptop? Show your work and explain your answer.





26. Two fair number cubes are rolled and the products of the outcomes are determined. The table shows allpossible outcomes for the products.

Part ABased on the table, what is the probability that the product is greater than 10, given that a 6 lands face-upon the first number cube? Explain your work.

Part BBased on the table, what is the probability that the product is even or a multiple of 5? Show your work.





27. The graph shows the data the students in a botany class recorded for the height of a plant over severaldays.

The students were instructed to fit a function h to describe the height of the plant after t days. The teacherinformed the class to use the point and one other point to create their function. The students werealso instructed to assume that the plant kept growing as the graph indicated for the next two days.

Part AA student used point and point to write a linear function to fit the data. Write the equation ofthat function. Show and explain your work.

Part BAnother student used point as the vertex of a parabola that contained the point to write aquadratic function to fit the data. Write the equation of the quadratic function. Show and explain yourwork.

Part CUse the functions from Part A and from Part B to determine the projected height of the plant after 32 daysfor each function. Show and explain your work.

Part DBased on your results in Part C, which function better fits the data? Explain your answer.





28. The two-way frequency table shows survey results for how many hours students at a high school workedon average each week last summer by grade.

What is the difference between the probability that a junior worked an average of 10 to 19 hours eachweek and the probability that a freshman worked an average of 20 to 29 hours each week? Round youranswer to the nearest hundredth.

Type your answer in the box.You may use numbers, symbols, and/or text in your answer.

29. Consider the given Venn diagram.



What is


30. A group of students participated in snow activities over winter break. The table shows the numbers ofgirls and boys and which type of snow activities they participated in.



What is the value of ?


31. A business owner asked all 60 of her employees to put their names on cards for a prize drawing. Sheplans to randomly select one employee for the prize. The table shows the distribution of the employees bygender and age.

The following are events in this situation.

Explain whether the events F and Y are independent.




32. The 2010 United States Census reported that the state of Georgia had 9,687,653 citizens. A statisticsteacher asked teams of her students to gather information about those citizens. The information was toinclude characteristics of the population not necessarily found in the actual census.

Part ATeam A decided to ask 100 adult females the number of hours they spent each week shopping forgroceries. What is one method the team could use to select the females for this study? Are there anydrawbacks to the method you described?

Part BTeam B wanted to compare the number of times a citizen visited a national park to the number of times heor she visited a state park. What type of statistical study is this? Explain your answer.

Part CTeam C used a graph produced by the Census Department to determine whether the distribution for genderand age of the senior citizens in their town was the same as that of the state at large. The graph they usedis shown below.

The team's report stated: "In our town, 128 males are 80 years old or older and 97 females are 80 years orolder." What can be concluded about the distribution of gender and age in the students' town compared tothat of the state? Explain your answer.





33. The board of directors of a large aviation museum wanted to find ways to increase the donations madeto the museum. They wondered whether having patriotic music playing in the background would affect thegenerosity of visitors.

●The days were selected at random.

●Patriotic music was played during 30 out of 60 days.

●At the end of the experiment the daily donation totals were compared.The table shows the results of the experiment.

Part AWhat kind of study was this? Why was it necessary to select the days randomly? Give an example tosupport your answer.

Part BCompare the center and spread of the two data sets. What does this information tell you about the dailydonations?

Part CBased on the data, what recommendations would you give the board of directors? Justify your answer.

Part DWhat additional information would a graph of the data give about the situation?





34. Two groups in a class took the same quiz. The results of each group are shown.

The difference between the interquartile ranges of the two groups is 7.5. Write an equation that can beused to find x, the first quartile of Group B.


35. Test scores for a sample of individuals are normally distributed. The mean is 125 and 2.5% of the scoresare above 161. What is the standard deviation?




36. Carol rolled a fair number cube labeled 1 through 6 ten times. The table shows her results.

Carol stated the probability of rolling a 5 is 0. Explain how Carol should modify her experiment so that theresult of rolling a 5 is better aligned with its theoretical probability.


37. The chart shows the sample size and description of a study.



After 5 years, the vision of each person was re-examined. The results were analyzed and interpreted, andconclusions were drawn. Explain how randomization was used as a method of control in this study.


38. A professor of environmental horticulture conducted a randomized experiment to determine the effectsof the amount of sunlight on the weight, in grams, of small cherry tomatoes. The two treatment groupsconsisted of 40 tomatoes chosen from plants grown in direct sunlight and 40 tomatoes chosen from plantsgrown in 70% sunlight. Statistics from the professor’s report are shown in the table.

A summary of the professor’s findings included a 95% confidence interval for the difference inthe mean weights of the two groups. What conclusion can be supported based on this confidence interval?




39. The table shows the number of pre-owned vehicles at an auto dealership that went through a safetyinspection.

The manager stated, “More trucks than cars passed the safety inspection.” Write a statement, using thedata from the table, which would more accurately compare the results of the safety inspection.




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