AP Stats
1. An observational study based on survey data concluded that individuals who took more vitamin C were able to recover from the flu faster. You want to replicate this study using an experimental approach. The treatment in this experiment might be:
A. how long it takes to recover from the flu, in days.
B. whether an individual took vitamin C in a pill form or liquid form.
C. the amount of vitamin C taken per day: 0 mg, 1000 mg, 2000 mg, or 3000 mg.
D. the change in body temperature over the period of the experiment.
E. All are acceptable treatments
2. Many statisticians say that the US Census, which attempts to count every population member directly, is significantly less accurate than a count estimated by random sampling. Why might a count estimated from random samples be more accurate than a census?
A. Random samples are scientific whereas censuses are not.
B. A true census takes so long that by the time all population members are counted,
the population has changed.
C. A census often can’t find every population member,
so some groups (such as the homeless) are often under-represented.
D. A census is a haphazard sample, and census takers may be bribed by households.
E. A census is an old method written into law before anyone knew anything about statistics.
3. In a survey of public opinion concerning state aid to a particular city, every 50th person registered as a voter was interviewed, beginning with a person selected at random from the first 50 listed.
Which sampling method was used?
A. simple random B. systematic C. stratified D. cluster E. voluntary response
4. A talk show host recently reported that in response to his on-air question, 82% of the more than 2500 e-mail messages received through his publicized address supported the death penalty for
anyone convicted of selling drugs to children. Which is the following is true?
A. The survey is meaningless because of voluntary response bias.
B. No meaningful conclusion is possible without knowing something
more about the characteristics of his listeners.
C. The survey would have been more meaningful if he had picked
a simple random sample of the 2500 listeners who responded.
D. The survey would have been more meaningful if he had used a control group.
E. This was a legitimate sample, randomly drawn from his listeners, and of sufficient size to
be able to conclude that most of his listeners support the death penalty for such a crime.
5. A researcher plans a study to examine the long-term confidence in the US economy among the adult population. She obtains a simple random sample of 30 adults as they leave the Wall Street
building one weekday afternoon. All but two of the adults agreed to participate in the survey.
Which of the following are true statements?
I. Proper use of chance as evidenced by the SRS makes this a well-designed survey.
II. The high response rate makes this a well-designed survey.
III. Convenience bias makes this a poorly designed survey.
A. I only B. II only C. III only D. I and II E. None of these are true
6. Which of the following is the best representative sample of the adult population in the U.S.?
A. Simple random sample of 10000 adults from different city phone books
B. Simple random sample of 10000 voters from across the country
C. Sample of 50000 individuals at the Super Bowl (which draws from all over the country)
D. Simple random sample of 1000 adults from across the country
E. Sample of 50000 members of AARP (American Association of Retired Persons)
7. Blocking in an experiment is best described as:
A. the use of chance to divide experimental units into groups.
B. a design in which neither the experimenter nor the subject knows who is in the treatment group
and who is in the control group
C. the tendency of subjects to respond favorably to any treatment.
D. the policy of repeating an experiment on different subjects to reduce chance variation and to
determine the generalizability of the findings.
E. a group of subjects that are similar in some way known to affect the response to the treatment.
8. Replication is best described as:
A. the use of chance to divide experimental units into groups.
B. a design in which neither the experimenter nor the subject knows who is in the treatment group
and who is in the control group.
C. a group of subjects that are similar in some way known to affect the response to the treatment
D. repeating an experiment on different subjects to reduce chance variation and to
determine the generalizability of the findings.
E. the tendency of subjects to respond favorably to any treatment.
9. Double-blind is best described as:
A. the use of chance to divide experimental units into groups.
B. a design in which neither the experimenter nor the subject knows who is in the treatment group
and who is in the control group
C. a group of subjects that are similar in some way known to affect the response to the treatment
D. repeating an experiment on different subjects to reduce chance variation and to
determine the generalizability of the findings.
E. the tendency of subjects to respond favorably to any treatment.
10. The placebo effect is best described as:
A. the use of chance to divide experimental units into groups.
B. a design in which neither the experimenter nor the subject knows who is in the treatment group
and who is in the control group
C. a group of subjects that are similar in some way known to affect the response to the treatment
D. the policy of repeating an experiment on different subjects to reduce chance variation and to
determine the generalizability of the findings.
E. the tendency of subjects to respond favorably to any treatment.
11. In one study on the effects of eating meat on the weight level, 500 subjects who admitted to eating meat at least once a day had their weights compared with those people who claim to be
vegetarians. In a second study, 500 randomly chosen subjects were served at least one meat meal
per day for 6 months, while 500 others were randomly chosen to receive a strictly vegetarian diet
for 6 months, with weights compared after 6 months.
A. The first study is a controlled experiment, while the second is an observational study.
B. The first study is an observational study, while the second is a controlled experiment.
C. Both studies are controlled experiments.
D. Both studies are observational studies.
E. Each study is part-controlled experiment and part observational study.
12. Which is a key distinction between well-designed experiments and observational studies?
A. More subjects are available for experiments than for observational studies
B. Ethical constraints prevent large-scale observational studies
C. Experiments are less costly to conduct than observational studies.
D. Experiments can show a cause-and-effect relationship whereas observational studies can’t.
E. Observational studies do not produce data that can be analyzed.
13. To test whether extensive exercise lowers the resting heart rate, a study is performed by randomly selecting half of a group of volunteers to exercise one hour each morning, while the rest are
instructed to perform no exercise. Is this study an experiment or an observational study?
A. an experiment with a control group
B. an experiment with blocking
C. an experiment which incorporates blinding
D. an observational study with little if any bias
E. an observational study with comparison and randomization
14. Twenty men and twenty women with high blood pressure were subjects in an experiment to
determine the effectiveness of a new drug in lowering blood pressure. Ten of the twenty men and
ten of the twenty women were chosen at random to receive the new drug. The remaining men
and women received the placebo. The change in blood pressure was measured for each subject.
What design is used for this experiment?
A. completely randomized with one factor, drug
B. completely randomized with one factor, gender
C. randomized, blocked by gender
D. randomized, blocked by drug
E. randomized, blocked by gender and drug
15. An experiment is conducted in which a series of tests are performed on pairs of identical twins
who were raised separately. A comparison of scores on each pair of twins is used for analysis. This
is best described as:
A. a matched-pairs procedure
B. a double-blind procedure
C. a randomized treatment group procedure
D. a procedure with two explanatory variables
E. an example of the placebo effect
16. You’re going to test two new varieties of fish food vs. a commonly used fish food. You set up an experiment as follows: 60 fish are randomly assigned to each of three different tanks. One tank is randomly selected to receive one of the new foods, another to receive the other new food, and the third tank to receive the common food. Fish growth is measured over time. This is an example of:
A. a randomized block design
B. a double-blind matched pairs test
C. a completely randomized design with no control group
D. a comparative block design
E. a completely randomized design with a control group
17. Let’s say you’re interested in the effects on boys of different dosage levels of a new drug for
the treatment of ADD. You set up an experiment to consider the factor of dosage with two levels
(300 mg vs. 500 mg). What would be the different treatment groups of the experiment within each
block?
A. Three groups: no drug/300 mg of new drug/500 mg of new drug
B. Three groups: placebo drug/300 mg of new drug/500 mg of new drug
C. Two groups: 300 mg of new drug/500 mg of new drug
D. Four groups: no drug/placebo drug/300 mg of new drug/500 mg of new drug
E. Two groups: placebo drug/either 300 or 500 mg of new drug
18. As primary research for one of her books, Shere Hite distributed 100,000 questionnaires to women’s groups: 4,500 women responded. Hite found that 96% of the women felt they give more emotional support to than they get from their husbands or boyfriends. Which of the following best describes her sample?
A. Representative sample
B. Voluntary response sample
C. Stratified random sample
D. Systematic sample
E. Cluster sample
19. An important reason a market researcher collects data using a stratified random sample rather than a simple random sample is:
A. to collect data at a lower cost.
B. to eliminate, or at least reduce, bias.
C. to make a representative sample more likely than one produced by simple random sampling.
D. convenient data collection.
E. to have a systematic way of obtaining the data.
20. All of the following are examples of a sample that suffers from an under-coverage bias except:
A. an estimate of an election outcome based on a sample of voters’ names taken from automobile
registrations.
B. a poll on Missouri dentists’ attitudes, based on questionnaires sent to a registry of attendees at
the largest dental convention in the state.
C. the mean income of US citizens, based on Census data.
D. a random sample of 5,000 US adults with survey data collected via e-mail.
E. a simple random sample of licensed drivers, taken from driver-licensing records.
21. Consider a survey in which 79% of the respondents said yes to the following question:
Agree or disagree: Since our economy can’t sustain itself without a healthy environment, it’s important that Congress pass laws to protect the environment. What’s a reasonable reaction to the survey results?
A. They’re not valid, due to response bias.
B. They’re not valid, due to voluntary response bias.
C. They’re not valid, due to under-coverage bias.
D. I totally agree. We need laws that protect the environment.
E. I disagree. We don’t need laws that protect the environment.
22. A firm administers a survey in the state of New York. The survey is mailed out to a random set of 5,000 households throughout the state, and responses are received from 200 households. The two key questions on the survey are:
1) Whom do you plan to vote for in the upcoming Senate election?
2) Do you agree with the idea of imposing term limits on the amount of time a Senator can spend in office?
What is a possible problem with this survey?
A. Voluntary response bias B. Under-coverage bias C. Response bias
D. Stratified original sample E. All of the above
23 If subjects in an experiment are separated into groups of whites and non-whites prior to the random assignment stage, we should think of race as a (an):
A. bias
B. blocking variable
C. matched pair
D. explanatory variable
E. response variable
24. For a survey regarding the food in the cafeteria, every 20th student to arrive at school was interviewed. This is an example of:
A. Simple random sampling
B. Stratified sampling
C. Cluster sampling
D. Systematic sampling
E. None of these
25. To determine if the generic brand of pet food is better than the store brand, researchers randomly assign the generic brand to a group of 50 dogs and randomly assign the store brand to a group of 45 cats. Is this a good experimental design?
A. Yes, because there was a control group
B. Yes, because it was blocked by type of pet
C. No, because more than two brands should have been tested
D. No, because more than two types of pets should have been used
E. No, because brand is confounded with type of pet
26. Which of these are categorical data?
A. The birth weights of anteaters
B. The lengths of anteaters
C. The different types of anteaters
D. The top speeds of anteaters
E. The prices of anteaters
27. Which of the following would be a categorical variable?
A. time required to complete the Boston Marathon
B. brand of soda most often purchased
C. weights of automobiles
D. average mileage for motorcycles
E. none of these
FOR QUESTIONS 28-29, use the stem plot below:
Home Runs per team at midseason
7 | 1 7 8|5 represents
8 | 5 6 7 8 85 homeruns
9 | 0 1 2 5 9
10| 1 3
11| 1
12| 2
13| 0
28. Which best describes the data?
A. skewed; mean greater than median
B. skewed; mean less than median
C. symmetric; mean greater than median
D. symmetric; mean equal to median
E. symmetric with outliers
29. Find the IQR for the number of Home Runs per team at midseason
A. 17 B. 15.5 C. 59 D. 86.5 E. 91.5
30. Which of the following graphical displays are used for quantitative data?
A. pie chart B. bar chart C. histogram D. frequency table E. all of these
31. Which of the following would most likely be graphed as a bar graph rather than a histogram?
A. The number of blue, red, black, and white cars in a random sample of 500 cars
B. The number of students in a mid-size university who own Macintosh or PC computers
C. The ethnic distribution for a major city
D. The number of people in various management positions at a large electronics store
E. All of the above
FOR QUESTIONS 32–34: The final point spreads (differences between winning scores and losing scores) for 25 major college football games were recorded in the stem-and-leaf display:
32. How many of the football games ended in a tie? 0 | 0 3 3 7 7 7
A. 0 1 | 0 0 3 4 4 6 7 7 8
B. 1 2 | 1 3 4 7 7 9
C. 2 3 | 2 4
D. 3 4 | 6
E. cannot be determine 5 | 3 7|6 = 76 points
33. Which of the following best describes the data?
A. Skewed distribution; mean greater than median
B. Skewed distribution; mean less than median
C. Symmetrical distribution; mean greater than median
D. Symmetrical distribution; mean less than median
E. Symmetrical distribution with outliers on high end
34. Find the median.
A. 7 B. 17 C. 16 D. 21 E. 24
FOR QUESTIONS 35 – 36, refer to the following stem plot:
35. Which league has the team that had hit the most home
runs by midseason, and how many home runs had that
team hit? Which league had the team with the fewest home runs?
A. American, 149, National
B. National, 116, American
C. National, 149, American
D. American, 118, American
E. American, 149, American
36. How many fewer home runs did the team with the fewest
home runs in the American League have than the team with
the fewest home runs in the National League?
How many more home runs did the team with the highest
home runs in the American League have than the highest team in the National League?
A. 2, 798
B. 4, 25
C. 14, 33
D. 4, 33
E. 14, 35
37. Consider these eight observations: {11,6,2,5,8,4,4,9}. What is the mean?
A. 8.167
B. 5.5
C. 4
D. 6.875
E. 6.125
38. Consider these eight observations: {11,6,2,5,8,4,4,9}. What is the median?
A. 6.5
B. 6.125
C. 5.5
D. 5
E. 6
39. Since the distribution of housing prices in a community is usually skewed right, which measure of center should you use for housing prices?
A. Mean
B. Median
C. Mode
D. Outlier
E. None of the above
40. Calculate, to the nearest whole number, the sample standard deviation of this data set:
{71, 75, 65, 73, 69, 77, and 67}.
A. 2 B. 4 C. 6 D. 8 E. 10
41. The box plot given below represents a distribution that is:
A. right skewed
B. left skewed
C. symmetrical
D. uniformly distributed
E. None of the above
42. Which statement is true given these box-plots comparing pulse rates before and after exercising? Include the outlier.
A. The ranges of pulse rates are the same before and after exercise
B. More than 50% of the pulse rates for before were less than the minimum for after exercise
C. There was more variation in the middle 50% of pulse rates after exercising
D. The pulse rates after exercising were always higher than before
E. There were no outliers in either case
43. Which of the following measurements are resistant to outliers?
I. mean II. median III. standard deviation IV. IQR
A. I only B. III only C. I and V D. II and III E. II and IV
44. A teacher gives a quiz to his 20 students and calculates the mean and standard deviation
as = 7.5 and s = 2.1. The teacher decides to increase everyone’s score by 5 points. What are the new mean and standard deviation?
A. = 7.5 ; s = 2.1
B. = 12.5 ; s = 2.1
C. = 7.5 ; s = 7.1
D. = 12.5 ; s = 7.1
E. cannot be determined
45. The following hypothetical data set shows the purchase price (in thousands) for a sample of
3-bedroom, 2-bathroom homes in Essex County, MA over the past year. Compute the five-number summary for a box plot. How many outliers are present in this distribution?
250, 254, 320, 342, 221, 235, 210, 426, 210, 298, 231, 254, 278, 234, 236, 235, 300, 401, 129,
234, 235, 235, 245
A. 0
B. 1
C. 2
D. 3
E. 4
FOR QUESTIONS 46 – 50 refer to the data in the table below:
46. What is the median for the data in the table?
A. 308 B. 306.5 C. 316.5
D. 302 E. 294
47. What is the upper quartile for the data in the table?
A. 322.5 B. 294 C. 336
D. 316 E. 319.5
48. What is the lower quartile for the data in the table?
A. 289 B. 296 C. 296.5
D. 294 E. None
49. What is the interquartile range for the data in the table?
A. 12.5 B. 5 C. 25.5 D. 47 E. –25.5
50. Based on the data in the table, which of the following would be an outlier?
A. 268.25 B. 332.25 C. 268.5 D. 255 E. None of the above
51. In Block 1, the average for the exam was 85% for 19 students. In Block 2, the average was 89% for 17 students. What was the overall average for the two classes?
A. 89%
B. 87%
C. 86.9%
D. 85%
E. not given enough information to calculate
52. Last weekend police ticketed 18 men whose mean speed was 72 miles per hour, and 30 women going an average of 64 mph. Overall, what was the mean speed of all ticketed?
A. 67 mph B. 68 mph C. 69 mph D. 72 mph E. cannot be determined
53. Why is the IQR considered to be a resistant statistic?
A. Adding a new extreme observation has little effect on it.
B. It’s equivalent to the distance from Q1 to the median, a resistant measure.
C. Adding an outlier changes the IQR dramatically.
D. It uses the mean in its calculation.
E. None of the above
54. Which measure of central tendency and measure of variation should be used with a normally
distributed distribution?
A. The mean and standard deviation
B. The mean and interquartile range
C. The median and interquartile range
D. The median and standard deviation
E. The mode and interquartile range
55. Which of the following can you determine or calculate from a stem plot?
I. Symmetry II. Gaps III. Clusters IV. Outliers
A. I, II, and III
B. I, II, and IV
C. I, III, and IV
D. II, III, and IV
E. I, II, III, and IV
56. Which of the following can outliers affect significantly?
I. Mean II. Median III. Standard deviation IV. Range V. Interquartile range
A. I, III, and V
B. II and IV
C. I and V
D. I, III, and IV
E. None of these choices give the correct combination of answers
57. Consider the following parallel box plots indicating the starting salaries (in thousands of dollars)
of blue collar and white-collar workers at a particular production plant.
Which of the following are true statements?
I. The ranges are the same.
II. The interquartile ranges are the same.
III. Half of the Blue-Collar salaries are less than the minimum White-Collar salary.
A. I only B. II only C. I and II D. I and III E. II and III
58. What does a z-score of 2 mean for a test?
A. You missed 2 questions
B. You got twice as many correct as average
C. Your grade was 2 points above average
D. Your grade was 2 standard deviations above average
E. Your IQ is 2 points higher than “normal”
FOR QUESTIONS 59-60, use the Empirical Rule for a population of bolts has a mean thickness of 20 millimeters, with a population standard deviation of 0.01 millimeters.
59. Give a minimum and maximum thickness that includes 68% of the population of bolts.
A. 20.00 to 20.02 millimeters
B. 19.00 to 21.00 millimeters
C. 19.98 to 20.02 millimeters
D. 19.99 to 20.01 millimeters
E. 19.97 to 20.03 millimeters
60. Give a minimum and a maximum thickness that will include 95% of the population of bolts.
A. 19.98 to 20.02 millimeters
B. 19.99 to 20.01 millimeters
C. 19.97 to 20.03 millimeters
D. 19.8 to 20.2 millimeters
E. These can’t be accurately computed.
61. Using the empirical rule, you can assume that what percent of the normal distribution is outside two standard deviations of the mean in both directions?
A. 0.3%
B. 50%
C. 5%
D. 95%
E. Can’t be calculated
62. The distribution of scores on a reading exam are approximately normal with mean = 50
and standard deviation = 10. What is a reasonable estimate of the highest score on the exam?
A. 40 B. 60 C. 80 D. 100 E. cannot be determined
63. The GRE test is widely used to predict the performance of applicants to graduate schools. The range of possible scores on the GRE is 200 to 900. A large university finds that the scores
of its applicants on the quantitative part are approximately normal with and .
Determine the proportion of applicants whose scores are between 480 and 680.
A. 0.2767 B. 1.3204 C. 0.9066 D. 0.6214 E. 0.6390
64. Company A manufacturing bomb fuses that burn an average of 50 minutes with a standard
deviation of 10 minutes. Company B manufactures bomb fuses that burn an average of 55
minutes with a standard deviation of 5 minutes. Which company’s fuse is most likely to burn
more than one hour? Assume all times are normally distributed.
A. Company A because it has a greater standard deviation.
B. Company B because it has a greater mean.
C. For both companies, the probability their fuse will last at least one hour is 16%.
D. For both companies, the probability their fuse will last at least one hour is 84%.
E. There is not enough information given to answer this question.
FOR QUESTIONS 65 – 68:
You measured the weights of members of population W and found the weights to be normally distributed. The distribution has a population mean weight of 160 pounds and a population standard deviation of 25 pounds.
65. For population W, find the z-score associated with a weight of 120 pounds.
A. z = – 2.6 B. z = – 1.0 C. z = – 1.6 D. z = 1.0 E. z = 1.6
66. For population W, what is the percentile for the weight 160 pounds?
A. 50 th B. 10 th p C. 30 th D. 75 th E. 90 th
67. Which is a reasonable estimate for the smallest weight in this population?
A. 60 lbs B. 85 lbs C. 110 lbs D. 135 lbs E. 160 lbs
68. In population W, what is the probability that a randomly selected subject will weigh between 140 and 180 pounds?
A. 0.202 B. 0.5 C. 0.677 D. 0.950 E. 0.576
69. The distributions of scores on exams A, B, and C are normal and have the given statistics.
Allen takes exam A, Bill takes exam B, and Cullen takes exam C. Each earns a grade of 83.
Rank them from lowest to highest according to their percentile.
A. B, C, A B. A, B, C C. C, B, A
D. C, A, B E. B, A, C
FOR QUESTIONS 70-71: Population H is a group of women with normally distributed heights. Population H has a population mean of 66 inches and a population standard deviation of 2.5 inches.
70. In population H, what is the height, to the nearest tenth of an inch, of the 70th percentile?
A. 67.3 inches B. 67.0 inches C. 64.7 inches
D. 66.0 inches E. 63.0 inches
71. In population H, what is the z-score, to the nearest tenth, associated with the height 65 inches?
A. z = -1.0 B. z = -0.5 C. z = 0.4
D. z = -0.4 E. z = 1.4
72. To the nearest whole number, what percentile is associated with z = -0.68?
A. 10 th percentile B. 40 th percentile C. 50 th percentile
D. 25 th percentile E. 75 th percentile
73. To the nearest whole number, what percentile is associated with z = 1.2?
A. 12 th percentile B. 25 th percentile C. 50 th percentile
D. 75 th percentile E. 88 th percentile
74. What area, to the nearest whole percent, of the normal curve is located between
z = -0.6 and z = 1.4?
A. 64% B. 91% C. 27% D. 50% E. 95%
FOR QUESTIONS 75-79: Applicants to a college psychology department have normally distributed GRE scores with a mean of 544 and a standard deviation of 103. Round to the nearest whole number.
75. What percentage of applicants scored between 500 and 700?
A. 50% B. 60% C. 70% D. 80% E. 90%
76. What percentage of applicants scored above 450 on the GRE?
A. 82% B. –82% C. 26% D. 11% E. 1%
77. What percentage of applicants had a GRE score below 625?
A. 78% B. –24% C. 24% D. 22% E. 5%
78. What is the GRE score at the 77th percentile?
A. 468 B. 505 C. 620 D. 1 E. -1
79. Find the GRE score at the upper quartile, Q3.
A. 1 B. 475 C. 470 D. 600 E. 613
80. Find the z-score for the lower quartile of any normal curve. Round to the nearest hundredth.
A. 0.67 B. 0.1 C. –0.1 D. –0.67 E. 0.33
81. Justin Hunter has an 80% chance of making his shot in a shoot-out. Which plan could be used to simulate the number of shots he would make in his next 3 attempts?
I. Let 1, 2, 3 represent making the first, 4, 5, 6 making the second and 7, 8, 9 making the third.
Generate 3 random numbers, ignoring repeats
II. Let 0, 1 represent making a shot and 2, 3, …9 missing a shot. Generate 3 random numbers
and count how many are in 2-9, ignoring repeats
III. Let 0, 1 represent missing a shot and 2, 3, …9 making a shot. Generate 3 random numbers
and count how many are in 2-9
A. I only
B. II only
C. III only
D. II and III
E. none of these are set up correctly
FOR QUESTIONS 82 – 85 refer to the following data:
The table below shows the results of a survey on participation in sports activities by men and women. Those surveyed answered yes to activities they had done at least twice in the previous 12 months.
82. If you randomly select one man, what’s the probability that he hunts, expressed as a percentage?
A. 0.1697 B. 16.97% C. 16.02% D. 0.1602 E. 8.24%
83. If you randomly select one woman, what’s the probability that she does aerobics?
A. 0.034 B. 0.169 C. 0.201 D. 0.087 E. 5.917
84. If you randomly select one man, what the probability that he doesn’t do exercise walking?
A. 0.231 B. 1.300 C. 0.400 D. 0.600 E. 0.769
85 If you randomly select one person from the study, what would be the probability that he or she plays baseball?
A. 0.1156 B. 0.0257 C. 0.0693 D. 0.0707 E. 0.0347
FOR QUESTIONS 86 AND 87: Suppose P(A) = 0.3 and P(B) = 0.2 .
86. What is P(A or B) if A and B are mutually exclusive?
A. 0.44 B. 0.06 C. 0.50 D. 0.10 E. 0.60
87. What is P(A and B) if A and B are independent?
A. 0.44 B. 0.06 C. 0.50 D. 0.10 E. 0.60
88. If P(A|B) is equal to P(A) then which of the following is true?
A. A and B have the same probability
B. A and B are supplementary
C. A and B are complementary
D. A and B are mutually exclusive
E. A and B are independent
89. Suppose that for a certain Caribbean Island in a 3-year period the probability of a major
hurricane is 0.25, the probability of water damage is 0.44 and the probability of both is 0.22.
What is the probability of water damage given that there is a hurricane?
A. 0.47 B. 0.50 C. 0.69 D. 0.88 E. 0.91
90. According to one poll, 12% of the public favor legalizing all drugs. A random sample of 6
people is chosen. What is the probability that at least one of them favors legalizing all drugs?
A. 0.380 B. 0.464 C. 0.536 D. 0.620 E. 0.844
FOR QUESTIONS 91 AND 92: In a certain city, 6% of teenagers are married, 25% of married teenagers have children, and 15% of unmarried teenagers have children.
91. A teenager is chosen at random. What is the probability the teenager has a child?
A. 0.156 B. 0.200 C. 0.400 D. 0.310 E. 0.904
92. A teenager is chosen at random. What is the probability the teenager is not married, given that
the teenager has a child?
A. 0.156 B. 0.200 C. 0.400 D. 0.310 E. 0.904
FOR QUESTIONS 93-95: To study the relationship between car owner satisfaction and country of production, car owners were surveyed with the following results.
Level of Satisfaction
93. What is the probability that the person owns a Japanese car and is highly satisfied?
A. 0.100 B. 0.200 C. 0.488 D. 0.082 E. 0.500
94. What is the probability that the person owns an American car, given that s/he is highly satisfied?
A. 0.552 B. 0.356 C. 0.200 D. 0.500 E. 0.333
95. What is the probability that the person is an owner of a European car or highly satisfied?
A. 0.575 B. 0.450 C. 0.513 D. 0.250 E. 0.400
96. A prom committee is formed of 15 seniors (8 of whom are male) and 10 juniors (5 of whom are
male). What is the probability that a randomly chosen chairperson is male or a senior?
A. 1.120 B. 0.800 C. 0.750 D. 0.312 E. 0.500
97. One hundred students from McCullum High School were randomly selected and surveyed.
They were asked if they had seen the movies The Grinch and Unbreakable. Their responses
were recorded in the following chart. Based on these data, what is the probability that a randomly selected student will have seen both movies given that the student saw at least one of the movies?
A 0.100 B. 0.444 C. 0.500 D. 0.556 E. 0.900
98. Which of the following is an example of events that are mutually exclusive?
A. having brown hair; having blue eyes D. owning a cat; owning a dog
B. rolling a 1; rolling an even E. none of these
C. drawing a heart; drawing an ace
99. If you are dealt a hand of 5 cards, what is the probability that at least one is a heart?
A. 0.222 B. 0.237 C. 0.763 D. 0.778 E. 0. 918
100. A standard 6-sided die is rolled. What is the probability that the number rolled is even or less than 4?
A. 1 B. 0.83 C. 0.67 D. 0.5 E. 0
101. Two events, A and B, are independent if…
A. P(A) = P(A|B) D. P(A U B) = 1
B. P(A U B) = P(A) + P(B) E. P(A) = 1 – P(B)
C. P(A) = P(B)
102. A marketing survey indicates that 60% of the population owns an automobile, 30% owns a house and 20% owns both. What’s the probability of owning an automobile given a family owns a home?
A. 0.67 B. 0.50 C. 0.33 D. 0.20 E. 0
103. If P(A) = 7% and P(B) = 28%, find P(A U B) if A and B are mutually exclusive.
A. 0.02 B. 0.21 C. 0.33 D. 0.35 E. 0
104. Here are the results of a survey given to 100 students about whether they have seen the movies The Sandlot and Mean Girls. Based on the responses, what is the probability that a student has seen Mean Girls, given that he/she has seen at least one of the movies?
Mean Girls
The Sandlot
A. 0.60 B. 0.67 C. 0.89 D. 0.90 E. 1
FOR QUESTIONS 105-108: The two-way table gives frequencies of the combined simple events of color and size of marbles in a bag.
105. What’s the probability that a randomly selected marble will be blue or white?
A. 0.34 B. 0.16 C. 0.50 D. 0.18 E. 0
106. Find the probability of a randomly drawn marble being yellow, given that the marble is small.
A. 0.39 B. 0.64 C. 0.14 D. 0.37 E. 0.23
107. Find the probability of a randomly drawn marble being large or small, given the marble is black.
A. 0.35 B. 0.28 C. 0.22 D. 0.20 E. 0.80
108. Find the probability of a randomly drawn marble is blue or large.
A. 0.40 B. 0.38 C. 0.24 D. 0.16 E. 0.04
109. If Benny is a 62% free throw shooter, what’s the probability that his first miss is on the 4th shot?
Assume that each shot is independent of the next.
A. .148 B. .021 C. .034 D. .091 E. .238
110. If Benny is a 62% free throw shooter, what’s the probability that he makes 7 out of 10 shots?
Assume that each shot is independent of the next.
A. .035 B. .002 C. .232 D. .70 0 E. .043
111. Fill in the blanks. Suppose the probability of a baseball player getting a hit in an at bat is 0.3038. If the player bats 28 times during a week, his number of hits should be around ______ give or take_______. Assume each at bat is independent.
A. 2.4335 , 8.506 B. 8.506 , 5.9219 C. 8.506 , 0.3038
D. 28 , 2.4335 E. 8.506 , 2.4335
112. According to info please, 18.8% of the luxury cars manufactured are silver. If there are 800 luxury cars on a lot and the color of each is independent, how many would you expect to be silver?
A. 18.8 B. 80 C. 150.4 D. 160 E. 376.6
113. According to info please, 18.8% of the luxury cars manufactured are silver. If seven luxury cars are selected random and the color of each is independent, find the probability that no more than one is silver.
A. 0.054 B. 0.377 C. 0.390 D. 0.610 E. 0.946
114. The table shows the probability distribution for the number of refills customers typically get of their drink at a local restaurant. Find the expected number of refills based on this data.
A. 0 B. 0.85 C. 1 D. 1.5 E. 2.2
115. The distribution for random variable R has a mean of 40 and standard deviation of 8. Find the mean and standard deviation for 4R – 3.
A. 157; 32 B. 157; 29 C. 160; 32 D. 160; 29 E. 148; 20
116. The distribution for random variable R has a mean of 40 and standard deviation of 8. Find the mean and standard deviation for R1 + R2.
A. 48; 8 B. 56.6; 16 C. 56.6; 8 D. 80; 11.3 E. 80; 16
117. The average points scored by L. James in a game is 27.4 points with a standard deviation of 5.8 points. The average points scored by A. Davis is 24.1 with a standard deviation of 4.3 points. What is the standard deviation for their total points combined within a game?
A. 4.3 B. 5.8 C. 7.2 D. 10.1 E. 15.2
118. The average points scored by L. James in a game is 27.4 points with a standard deviation of 5.8 points. The average points scored by A. Davis is 24.1 with a standard deviation of 4.3 points. How many more points does L. James typically score, compared to A. Davis, and what is the standard deviation for the difference?
A. 1.5; 3 B. 3; 15.2 C. 3; 3.9 D. 3.3; 15.2 E. 3.3; 7.2
119. Given that X is a binomial random variable with n = 20 and p = 0.4, find P(X = 5).
A. 4.81x10-6 B. 0.010 C. 0.126 D. 0.075 E. 0.874
120. Given that X is a binomial random variable with n = 20 and p = 0.4, find P(X 6).
A. 4.81x10-6 B. 0.010 C. 0.126 D. 0.075 E. 0.874
121. Should a veterinarian offer specialized care for older cats? To answer this question, a random sample of 50 records of cats was selected and the average age based on the records was 8.2 years. Which of the following describes the value of 8.2?
A. Sample B. Statistic C. Population D. Parameter E. Census
122. A family has five children with ages 10, 12, 14, 18, and 20, which yields a mean age of μ = 14.8 years and a standard deviation of σ = 3.71 years. There are 25 different possible samples of size 2 children that can be selected from this population (sampling with replacement). Suppose that for each of these 25 samples, the sample mean is calculated. The distribution of these sample means will have a mean of μxˉ and a standard deviation of σxˉ .Which of the following statements is true?
A. μxˉ > 14.8 B. μxˉ < 14.8
C. μxˉ = 14.8 and σxˉ > 3.71 D. μxˉ = 14.8 and σxˉ = 3.71
E. μxˉ = 14.8 and σxˉ < 3.71
123. The true parameter for some population distribution is 50. Simulations of 100 random samples, each of size n , are drawn from this population. For each simulated sample, there are five estimators that are calculated. The histograms below display the simulated sampling distributions for the five estimators. Which is the best estimator for the population parameter?
A. B.
C. D.
E.
124. A large university would like to estimate the starting salary of its recent graduates. They survey a random sample of 1000 graduates from list of alumni. Which of the following best describes the effect on the sampling distribution if the researchers decrease the sample size from 1000 to 500?
The bias will decrease and the standard deviation will remain the same.
The bias will increase and the standard deviation will remain the same.
The bias will remain the same and the standard deviation will decrease.
The bias will remain the same and the standard deviation will increase.
The bias will decrease and the standard deviation will decrease.
125. With the rise of online dating, are people going on more dates than they used to? To investigate this question, a research group randomly selected 200 adults who were signed up for at least one dating app. Using an anonymous questionnaire, they asked each person: “How many dates have you been on in the last year using a dating app?” The sample mean will be calculated from their responses. Will the sample mean (xˉ) be an unbiased estimator of the population mean (μ) ?
No, because the sample mean xˉ does not always equal the population mean μ .
No, because some people might be signed up for multiple dating apps.
Yes, because they only asked people who are signed up for at least one dating app.
Yes, because the sample size of 200 meets the Central Limit Theorem.
Yes, because for random samples, the mean of the sampling distribution of xˉ is equal to the population mean μ.
126. It is estimated the mean amount paid by residential customers in Texas for cable and internet is 114 per month. To see if this estimate is accurate, one internet service provider will select a random sample of 200 Texas residential customers and another internet service provider will select a random sample of 300 Texas residential customers. We want to calculate the probability that the mean is less than 100 per month. Which of the following statements is true?
It is less likely for a sample size of 300 people, because there is more variability in the sampling distribution for larger sample sizes.
It is less likely for a sample size of 300 people, because there is less variability in the sampling distribution for larger sample sizes.
It is less likely for a sample size of 200 people, because there is more variability in the sampling distribution for smaller sample sizes.
It is less likely for a sample size of 200 people, because there is less variability in the sampling distribution for smaller sample sizes.
They are equally likely, because the mean of the sampling distribution is the same for both sample sizes.
127. According to Ipsos’ Global Happiness report in 2024, 83% of adults in Mexico report being happy, while only 70% of adults in Spain report being happy. Assuming these estimates are true, which of the following is closest to the probability that the difference in proportions of adults who are happy (Mexico – Spain) is greater than 0.15 for a random sample of 250 adults from Mexico and a random sample of 500 adults from Spain?
A. 0.0480 B. 0.2619 C. 0.2752 D. 0.7381 E. 0.7248
128. A machine is set to fill containers with almonds. Assume the weights of the almonds in the containers are normally distributed with μ = 28 ounces and σ = 0.5 ounce. Nine packages are randomly selected from the containers that have been filled over the past hour. Which of the following best approximates the probability that the total weight of all 9 packages will be no more than 250 ounces?
A. 0.0913 B. 0.3284 C. 0.5000 D. 0.6716 E. 0.9088
129. A representative from the mayor’s office is investigating rent prices for studio apartments in Denver. The distribution of rent prices is approximately normal with a mean of $1,820 and a standard deviation of $20. The representative randomly selects a random sample of 25 studio apartments and records their rent prices. Which of the following best describes the sampling distribution of the sample mean rent prices for studio apartments in Denver for samples of size 25?
The shape is approximately normal, with mean $1,820 and standard deviation $20
The shape is approximately normal, with mean $1,820 and standard deviation $4
The shape is approximately normal, with mean $1,820 and standard deviation $0.80
The shape is unknown, with mean $1,820 and standard deviation $20
The shape is unknown, with mean $1,820 and standard deviation $4.
130. The police response time for robberies in San Diego varies with an average response time of
15.5 minutes. A random sample of 35 robberies in San Diego is selected, and the mean response time for the sample is calculated. Which of the following statements is justified by the central limit theorem?
The distribution of sample means of the response times is not approximately normal because the population mean response time of 15.5 minutes is not sufficiently large.
The distribution of response times for the sample is not approximately normal because the population mean response time of 15.5 minutes is not sufficiently large.
The distribution of response times for the sample is approximately normal because the sample size of 35 is sufficiently large.
The distribution of response times for the population is approximately normal because the sample size of 35 is sufficiently large.
The distribution of sample means of the response times is approximately normal because the sample size of 35 is sufficiently large.
131. Based on many years of sales data, a small retail store knows that the distribution of their daily sales is skewed right with a mean of $783 and a standard deviation of $106. Suppose a random sample of 36 days is selected and the sample mean daily sales is calculated. This process is repeated for total of 150 samples. Which of the following is the best description of the distribution of the 150 sample means?
Skewed right with a mean of $783 and a standard deviation of $106.
Skewed right with a mean of $783 and a standard deviation of $17.67.
Skewed right with a mean of $783 and a standard deviation of $8.65.
Approximately normal with a mean of $783 and a standard deviation of $17.67.
Approximately normal with a mean of $783 and a standard deviation of $8.65.
132. The distribution of annual medical expenses per household is strongly skewed right. If samples of size 30 are taken from the population distribution, which of the following statements about the sampling distribution of the sample mean medical expenses per household is true?
The mean and the standard deviation of the sampling distribution is approximately the same as the mean and the standard deviation of the population distribution.
The shapes of the sampling distribution and the population distribution are the same because the sample size is 30.
If the sample size were increased, the standard deviation of the sampling distribution would get closer and closer to the standard deviation of the population distribution.
If the sample size were increased, the shape of the sampling distribution would get closer to a normal distribution.
Because the sample size is 30, the population distribution is approximately normal.
133. The distribution of lengths of time that homeowners have owned their current homes in a certain town is approximately normal with a mean of 12.9 years with a standard deviation of 4.1 years. Nine homeowners are randomly selected from this population. What is the probability that the average length of time that these nine homeowners have owned their current house is greater than 14 years?
A. 0.0079 B. 0.2104 C. 0.3942 D. 0.7896 E. Essentially 0
134. In a long-term study conducted in Poland, it was found that the distribution of birth weights for full-term male babies has a mean of 3622 grams and a standard deviation of 432 grams. The distribution of birth weights for full-term female babies has a mean of 3465 grams and a standard deviation of 414 grams. Suppose a researcher selects independent random samples of 6 full-term male babies and 8 full-term female babies. Which of the following is closest to the standard deviation of the sampling distribution of the difference in sample mean weights?
A. 43262+41482 B. 4326+4148 C. 4326-4148
D. 43226-41428 E. 43226+41428
135. The distribution of height for the Mammoth sunflower variety at a farm is approximately normal with a mean height of 10 feet. The distribution of height for the Earthwalker sunflower variety at the farm is approximately normal with a mean height of 7.5 feet. Ten sunflowers of each variety are randomly selected, and the heights are recorded. Let xM be the sample mean height of the 10 Mammoth sunflowers and let xE be the sample mean height of the 10 Earthwalker sunflowers. Which of the following is the best interpretation of PxM-xE>1.75=0.20 ?
The probability that the sample mean height of the Mammoth sunflowers is at least 1.75 feet greater than the sample mean height of the Earthwalker sunflowers is 0.20.
The probability that the sample mean height of the Mammoth sunflowers is at least 0.20 feet greater than the sample mean height of the Earthwalker sunflowers is 1.75.
The probability that each of the 10 Mammoth sunflowers are at least 1.75 feet taller than the each of the 10 Earthwalker sunflowers is 0.20.
The probability of observing a difference greater than 1.75 feet between the height of a Mammoth sunflower and an Earthwalker sunflower is 0.20.
The probability that the sample mean height of the Mammoth sunflowers is greater than the sample mean height of the Earthwalker sunflowers is 0.20.