Semester 1 Exam Stats

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University of Texas, Rio Grande Valley *

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101

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Statistics

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Jan 9, 2024

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1. Grain moisture is a characteristic of grain that affects the price paid for the grain. A random sample of 28 loads of corn was evaluated for moisture as a percent of the total weight. A different random sample of 28 loads of soybeans was also evaluated for moisture. The data are displayed in the dotplots below. Based on the dotplots, which of the following is greater for the percent moisture of corn than for the percent moisture of soybeans? (A) The first quartile (B) The median (C) The third quartile (D) The range (E) The interquartile range 2. Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean years and standard deviation years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the percentile of the distribution? (A) years (B) years (C) years (D) years (E) years 3. A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies? (A) 15.1 (B) 15.3 (C) 16.3 (D) 16.5 (E) 16.7 AP STATISTICS Test Booklet Semester 1 Exam AP Statistics Page 1 of 7

4. For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season? (A) 250 yards (B) 300 yards (C) 350 yards (D) 400 yards (E) 450 yards 5. The distribution of weights of female college cross-country runners is approximately normal with mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who weigh between 114 pounds and 138 pounds? (A) 18% (B) 32% (C) 68% (D) 82% (E) 95% 6. The distribution of assembly times required to assemble a certain smartphone is approximately normal with mean 4.6 minutes and standard deviation 0.6 minute. Of the following, which is closest to the percentage of assembly times between 4 minutes and 5 minutes? (A) 34% (B) 41% (C) 59% (D) 68% (E) 95% 7. Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. What type of study was conducted, and what is the response variable of the study? (A) An experiment was conducted, and the response variable is the concentration of the chemical. (B) An experiment was conducted, and the response variable is the depth of the water. (C) A census was conducted, and the response variable is the depth of the water. (D) An observational study was conducted, and the response variable is the concentration of the chemical. (E) An observational study was conducted, and the response variable is the depth of the water. Test Booklet Semester 1 Exam Page 2 of 7 AP Statistics

8. As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study? (A) The population is the 770 students who were selected, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis. (B) The population is the 770 students who were selected, and the sample is whether each student in the survey uses the exercise facility on a regular basis. (C) The population is the 34,000 students who attend the university, and the sample is whether each student in the survey is male or female. (D) The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected. (E) The population is the 34,000 students who attend the university, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis. 9. The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city’s effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department? (A) A census (B) A sample survey (C) An experiment with a completely randomized design (D) An experiment with a randomized block design (E) An experiment with a matched-pairs design 10. For the purpose of determining the value of its end-of-year inventory, a clothing store creates a list at the end of the year of every item currently in stock along with each item’s wholesale price. Which of the following is the best description of the end-of-the-year activity? (A) An experiment, because the items are treatments and wholesale prices are responses. (B) An experiment, because the store does not know the total wholesale price of all the items. (C) A sample survey, because the store wants to estimate the value of all items for the entire year. (D) A sample survey, because the items currently in the store at the end of the year are a random sample of all items in the store for the entire year. (E) A census, because the wholesale prices of all items are listed. 11. A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample? Test Booklet Semester 1 Exam AP Statistics Page 3 of 7

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(A) Select all female students on the list. (B) Randomly select 50 students on the list. (C) Randomize the names on the list and then select every tenth student on the randomized list. (D) Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list. (E) Randomly select 50 students on the list who are attending college. 12. A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medicine. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of two groups of equal size. The first group received the current medicine and the second group received the new medicine. When a participant experienced a migraine, he or she was instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale from 1 to 10, with 1 being no relief to 10 being complete relief. At the end of six months, the average pain relief for each participant was calculated. Which of the following is the best description of the study? (A) An experiment using a completely randomized design (B) An experiment using a matched-pairs design (C) An observational study using a simple random sample (D) An observational study using a cluster sample (E) An observational study using a stratified sample 13. A study was conducted to evaluate the impact of taking a nutritional supplement on a person’s reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Which of the following is the best description of the study? (A) A randomized block design (B) A completely randomized design (C) A matched-pairs design (D) A randomized observational study (E) A stratified observational study 14. A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item? Test Booklet Semester 1 Exam Page 4 of 7 AP Statistics

(A) (B) (C) (D) (E) 15. The table shows the responses from people when asked if they support a proposal to expand the public library. Under the Age of Age or Older Total Yes No Total One person from those who responded will be selected at random. Which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age or older? (A) (B) (C) (D) (E) 16. Events D and E are independent, with P ( D ) = 0.6 and P ( D and E ) = 0.18. Which of the following is true? (A) P ( E ) = 0.12 (B) P ( E ) = 0.4 (C) P ( D or E ) = 0.28 (D) P ( D or E ) = 0.72 (E) P ( D or E ) = 0.9 Test Booklet Semester 1 Exam AP Statistics Page 5 of 7

17. Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table. What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ? (A) 0.40951 (B) 0.50000 (C) 0.59049 (D) 0.91854 (E) 0.99144 18. A city department of transportation studied traffic congestion on a certain highway. To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than . The probability distribution of the number of people in passenger cars on the highway is shown in the table. Number of people Probability Based on the probability distribution, what is the mean number of people in passenger cars on the highway? (A) (B) (C) (D) (E) 19. The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance? Test Booklet Semester 1 Exam Page 6 of 7 AP Statistics

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(A) $2.45 (B) $2.75 (C) $24.50 (D) $29.40 (E) $36.00 20. As part of a demographic study, a college administrator needed to survey a sample of students from the college. From each major offered at the college, the administrator randomly selected percent of the students with that major to participate in the survey. Which of the following is the best description of the type of sample selected by the administrator? (A) Cluster sample (B) Convenience sample (C) Simple random sample (D) Stratified random sample (E) Systematic random sample Test Booklet Semester 1 Exam AP Statistics Page 7 of 7

Semester 1 Exam Stats

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