AP Stats Final Review

27) Which of the following distributions has a mean of 60 and standard deviation of 4?

(A) With the left number at 48 and the right number at 72

86) A random variable Y has the following probability distribution: Y -1 0 1 2 P(Y) 4C 2C 0.07 0.03 The value of the constant C is: (A) 0.10 (B) 0.15 (C) 0.20 (D) 0.25 (E) 0.75

(B) 0.15

20) To which of the histograms below can the boxplot correspond?

(B) With the middle boxes adding up to the first box, at about 25%

60) Given two events, E and F, such that P(E)=.340,P(F)= .450, and P(E∪F)=.637, then the two events are: (A) independent and mutually exclusive. (B) independent, but not mutually exclusive. (C) mutually exclusive, but not independent. (D) neither independent nor mutually exclusive. (E) there is not enough information to answer the question.

(B) independent, but not mutually exclusive.

50) Suppose P(X)=.25 and P(Y)=.40. If P(X│Y)=.20, what is P(Y|X)? (A) .10 (B) .125 (C) .32 (D) .45 (E) .50

(C) .32

88) The probability that a child will have a problem with alcohol is 0.75 if at least one of the parents is an alcoholic and 0.05 if neither parent is an alcoholic. In a recent study of a large number of children, 5% of the children involved had at least one parent who is an alcoholic. If a child in this study has an alcohol-related problem, what is the probability that at least one of the parents of the child is an alcoholic? (A) 0.0375 (B) 0.0475 (C) 0.4412 (D) 0.7895 (E) 0.8000

(C) 0.4412

Questions 40 - 42 refer to this table: This two-way table gives frequencies of the combined simple events of color and size of marbles in a bag Blue Yellow White Black Total Small 27 34 16 10 87 Medium 7 19 53 13 92 Large 3 0 11 42 56 Total 37 53 80 65 235 40) 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) None of the above

(C) 0.50

75) The mean of a data set is 40 pounds and the standard deviation is 8 pounds. What value of an observation corresponds to a z-score of -1.25? (A) -30 (B) -50 (C) 30 (D) 32 (E) 50

(C) 30

69) A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5,000 with probability 9/20, to break even with probability 5/20, and to lose $5,000 with probability 3/20. The expected profit in dollars is (A) 1500 (B) 0 (C) 3000 (D) 3250 (E) -1500

(C) 3000

108) A large bakery has many different products for sale. Suppose that 70% of all customers of the bakery order donuts, 50% order cinnamon rolls, and 40% order both. If a customer is randomly selected, what is the probability that they ordered either donuts or cinnamon rolls but not both? (A) 20% (B) 24% (C) 40% (D) 48% (E) 60%

(C) 40%

64) 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

(C) 5%

89) The weights of newborn baby boys have an approximately normal distribution with a mean of 8.0 pounds and a standard deviation of 1.5 pounds. A doctor tells a mother that her newborn baby boy has a weight at the 25th percentile. Which of the following is closest to this baby's weight? (A) 2.00 pounds (B) 5.00 pounds (C) 7.00 pounds (D) 7.63 pounds (E) 8.90 pounds

(C) 7.00 pounds

12) Given these parallel boxplots, which of the following is incorrect? (A) The ranges are the same. (B) The interquartile ranges are the same. (C) Both sets are skewed to both lower and higher values. (D) Set A may not be symmetric. (E) Set A may have 100 times are many values as set B.

(C) Both sets are skewed to both lower and higher values.

81) A researcher is testing a company's new stain remover. He has contracted with 40 families who have agreed to test the product. He randomly assigns 20 families to the group that will use the new stain remover and 20 to the group that will use the company's current product. The most important reason for this random assignment is that (A) randomization makes the analysis easier since the data can be collected and entered into the computer in any order. (B) randomization eliminates the impact of any confounding variables. (C) randomization is a good way to create two groups of 20 families that are similar as possible, except for the treatments they receive. (D) randomization ensures that the study is double-blind. (E) randomization reduces the impact of outliers.

(C) randomization is a good way to create two groups of 20 families that are similar as possible, except for the treatments they receive.

53) The average noise level in a bar is 36 decibels with a standard deviation of 5 decibels. Assuming a normal distribution, what is the probability the noise level is between 30 and 40 decibels? (A) 0.327 (B) 0.337 (C) 0.381 (D) 0.673 (E) 0.683

(D) 0.673

25) The number of adults living in homes on a randomly selected city block is described by the following probability distribution. Number of adults, x 1 2 3 4 Probability, P(x) 0.25 0.50 0.15 0.10 What is the standard deviation of the probability distribution? (A) 0.50 (B) 0.62 (C) 0.79 (D) 0.89 (E) 2.10

(D) 0.89

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. 7) To the nearest whole number, what percentile is associated with z = -0.68? (A) 10th percentile (B) 40th percentile (C) 50th percentile (D) 25th percentile (E) 75th percentile

(D) 25th percentile

92) Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X>$400)? (A) 0.2119 (B) 0.2881 (C) 0.5319 (D) 0.7881 (E) 0.8450

(A) 0.2119

Use normal cdf to find

PERCENT when given z-score

71) A sample of production records for an automobile manufacturer shows the following figures for production per shift: 705 700 690 705 The variance of the sample is approximately (A) 8.66 (B) 7.07 (C) 75.00 (D) 50.00 (E) 20.00

VOID

Use InvNorm to find

Z-SCORE when given percent

A population of bolts has a mean thickness of 20 millimeters, with a population standard deviation of 0.01 millimeters. 58) Give, in millimeters, 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.

(A) 19.98 to 20.02 millimeters

4) Given that the median is 270 and the interquartile range is 20, which of the following statements is true? (A) Fifty percent of the data are greater than or equal to 270. (B) Fifty percent of the data are between 260 and 280. (C) Seventy-five percent of the data are less than or equal to 280. (D) The mean is between 250 and 290. (E) The standard deviation is approximately 13.5.

(A) Fifty percent of the data are greater than or equal to 270.

31) Suppose X and Y are independent random variables. The variance of X is equal to 16; and the variance of Y is equal to 9. Let Z = X - Y. What is the standard deviation of Z? (A) 2.65 (B) 5.00 (C) 7.00 (D) 25.0

(B) 5.00

82) 100 volunteers who suffer from anxiety take part in a study. 50 are selected at random and assigned to receive a new drug that is thought to be extremely effective in reducing anxiety. The other 50 are given an existing anti-anxiety drug. A doctor evaluates anxiety levels after two months of treatment to determine if there has been a larger reduction in the anxiety levels of those who take the new drug. This would be double blind if (A) both drugs looked the same (B) neither the subjects nor the doctor knew which treatment any subject had received (C) the doctor couldn't see the subjects and the subjects couldn't see the doctor (D) there was a third group that received a placebo (E) all of the above

(B) neither the subjects nor the doctor knew which treatment any subject had received

45) People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor? (A) 0 (B) 0.280 (C) 0.526 (D) 0.720 (E) 1

(C) 0.526

32) A company wishes to survey what people think about a new product it plans to market. They decide to randomly sample from their customer database as this includes phone numbers and addresses. This procedure is an example of which type of sampling? (A) Cluster (B) Convenience (C) Simple random (D) Stratified (E) Systematic

(C) Simple random

14) In which of the following histograms is the mean less than the median? (A) (B) (C) (D) (E)

(C) Skewed left diagram

66) A set of data has a mean that is much larger than the median. Which of the following statements is most consistent with this information? (A) The distribution is symmetric (B) The distribution is skewed left (C) The distribution is skewed right (D) The distribution is bimodal (E) The data set probably has a few low outliers

(C) The distribution is skewed right

38) 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.

(D) An observational study was conducted, and the response variable is the concentration of the chemical.

13) Which of the following is true about the areas described under the normal curve? (A) The area below the mean is greater than the area above the mean. (B) The area in the range from z = 0 to z = 1 is the same as the area in the range from z = 1 to z = 2. (C) Roughly 50% of the observations are located at the mean of the distribution. (D) Fewer than one percent of the cases are located three standard deviations above or below the mean. (E) 95% of the observations have values twice that of the mean.

(D) Fewer than one percent of the cases are located three standard deviations above or below the mean.

93) Which of the following random variables has a distribution which most closely resembles a normal distribution? (A) A random number between 0 and 9 from a table of single-digit random numbers (B) The number of car accidents in 1 month at a very rural intersection (C) The score of a student on a very easy 10-point quiz (D) The annual income of a U.S. citizen (E) The actual weight of a jar of peanut butter labeled as 16 ounces

(E) The actual weight of a jar of peanut butter labeled as 16 ounces

10) An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The boxplot below summarizes the records data for one year. Based on the bosplot, which of the following statements must be true? (A) The range of the number of on-time arrivals is greater than 90. (B) The interquartile range of the number of on-time arrivals is 22. (C) The number of days that had at least 80 on-time arrivals is greater than the number of days that had at most 76 on-time arrivals. (D) The number of days that had from 76 to 80 on-time arrivals is equal to the number of days that had at most 76 on-time arrivals. (E) The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.

(E) The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.

Questions 40 - 42 refer to this table: This two-way table gives frequencies of the combined simple events of color and size of marbles in a bag Blue Yellow White Black Total Small 27 34 16 10 87 Medium 7 19 53 13 92 Large 3 0 11 42 56 Total 37 53 80 65 235 41) 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

(A) 0.39

98) The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that •the probability of being awarded the first job (Event A) is 0.75; •the probability of being awarded the second job (Event B) is 0.5; and •the probability of being awarded both jobs (A and B) is 0.375. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B? (A) Event A and event B are mutually exclusive and are independent. (B) Event A and event B are mutually exclusive and are not independent. (C) Event A and event B are not mutually exclusive and are independent. (D) Event A and event B are not mutually exclusive and are not independent. (E) Event A and event B are not mutually exclusive, and independence cannot be determined with the information given.

(C) Event A and event B are not mutually exclusive and are independent.

95) Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10, On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class? (A) She scored much better on the first exam. (B) She scored much better on the second exam. (C) She scored about equally well on both exams. (D) It is impossible to tell because the class size is not given. (E) It is impossible to tell because the correlation between the two sets of exam scores is not given.

(C) She scored about equally well on both exams.

A population of bolts has a mean thickness of 20 millimeters, with a population standard deviation of 0.01 millimeters. 57) Give, in millimeters, 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

(D) 19.99 to 20.01 millimeters

15) A random sample of golf scores gives the following summary statistics: n=20, x ̅=84.5, S_x=11.5, minX=68,Q_1=78,Med=86,Q_3=91,maxX=112. What can be said about the number of outliers? (A) 0 (B) 1 (C) 2 (D) At least 1 (E) At least 2

(D) At least 1

90) The dotplot below displays the daily high temperature, in degrees Fahrenheit, for a city in the southeastern United States during the 28 days in the month of February 2014. Which of the following is closest to the percentile rank of a day in that month where the daily high temperature in this city was 70 degrees Fahrenheit? (A) 10 (B) 25 (C) 70 (D) 90 (E) 95

(E) 95

62) Rainwater was collected in water collectors at 30 different sites near an industrial complex and the amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. The following stemplot of the data was constructed Which of the following boxplots is a correct representation of the same distribution? (A) A (B) B (C) C (D) D (E) E

(E) E - Check Q1 and Q2, Check tails and ranges

33) The back-to-back stemplot on the right shows the number of books read in a year by a random sample of college and high school students. Which of the following statements are true? I. One college student read seven books. II. The college median is equal to the high school median. III. The mean is greater than the median in both groups. (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

(E) I, II, and III

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. 5) 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

(A) 67.3 inches

52) 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.

(A) A randomized block design

8) 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

(A) Adding a new extreme observation has little effect on it.

73) A researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child and found an approximately normal distribution with a mean age of 27.3 and a standard deviation of 5.4. According to the 68-95-99.7 rule, approximately 95% of women had their first child between the ages of (A) 11.1 years and 43.5 years (B) 16.5 years and 38.1 years (C) 21.9 years and 32.7 years (D) 21.9 years and 38.1 years (E) 25.0 years and 29.6 years

(B) 16.5 years and 38.1 years

78) A company determines the mean and standard deviation of the number of sick days taken by its employees in one year. Which of the following is the best description of the standard deviation? (A) Approximately the mean distance between the number of sick days taken by individual employees and the mean number of sick days taken by all employees. (B) Approximately the median distance between the number of sick days taken by individual employees and the median number of sick days taken by all employees. (C) The distance between the greatest number of sick days taken by an employee and the mean number of sick days taken by all employees. (D) The number of days separating the fewest sick days taken and the most sick days taken when considering all employees. (E) The number of days separating the fewest sick days taken and the most sick days taken when considering the middle 50 percent of the distribution.

(A) Approximately the mean distance between the number of sick days taken by individual employees and the mean number of sick days taken by all employees.

96) Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation? (A) Assign "0, 1, 2" as watching the shopping channel at least once a week and "3, 4, 5, 6, 7, 8, and 9" as not watching. (B) Assign "0, 1, 2, 3" as watching the shopping channel at least once a week and "4, 5, 6, 7, 8, and 9" as not watching. (C) Assign "1, 2, 3, 4, 5" as watching the shopping channel at least once a week and "6, 7, 8, 9, and 0" as not watching. (D) Assign "0" as watching the shopping channel at least once a week and "1, 2, 3, 4, and 5" as not watching; ignore digits "6, 7, 8, and 9." (E) Assign "3" as watching the shopping channel at least once a week and "0, 1; 2, 4, 5, 6, 7, 8, and 9" as not watching.

(A) Assign "0, 1, 2" as watching the shopping channel at least once a week and "3, 4, 5, 6, 7, 8, and 9" as not watching.

70) Control groups are used in experiments in order to ... (A) Control the effects of lurking variables such as the placebo effect. (B) Control the subjects of a study so as to insure all participate equally. (C) Guarantee that someone other than the investigators, who have a vested interest in the outcome, control how the experiment is conducted. (D) Achieve a proper and uniform level of randomization. (E) None of the above.

(A) Control the effects of lurking variables such as the placebo effect.

36) Which of the following statements is incorrect? (A) Voluntary response samples often underrepresent people with strong opinions. (B) Convenience samples often lead to undercoverage bias. (C) Questionnaires with nonneutral working are likely to have response bias. (D) There is no way to fix the results if a biased sampling method was employed. (E) Nonresponse bias should be avoided because those who do not respond might have different views from those who do respond.

(A) Voluntary response samples often underrepresent people with strong opinions.

35) Two antidepressants are to be compared in the treatment of elderly patients in a nursing home. Each patient has his or her own room, some with spectacular views of the ocean. The experimental design is to create homogeneous blocks with respect to window view. How should randomization be used for a randomized block design? (A) Within each block, randomly pick half the patients to receive each antidepressant. (B) Randomly pick half of all patients to receive each antidepressant, but then analyze the results separately by blocks. (C) Randomly choose which blocks will receive which antidepressants. (D) Randomly choose half the blocks to receive each antidepressant for a given time period; then for the same time period switch the medication in each block and compare the results. (E) For ethical reasons, allow patients to choose which medication they prefer taking, but them randomly assign patients to the blocks.

(A) Within each block, randomly pick half the patients to receive each antidepressant.

37) A critical difference between experiments and observational studies is (A) an experiment often suggests a causal relationship, whereas an observational study only suggests an association. (B) observational studies make use of randomization, whereas experiments do not. (C) experiments are generally more cost and time effective than observational studies. (D) tests of significance can be used on data collected from experiments but not on data collected from studies. (E) experiments are free to choose subjects from an entire population, whereas an observational study only considers a random sample.

(A) an experiment often suggests a causal relationship, whereas an observational study only suggests an association.

30) An advantage to using surveys as opposed to experiments is that (A) surveys are generally cheaper to conduct. (B) it is generally easier to conclude cause and effect from surveys. (C) surveys are generally not subject to bias. (D) surveys involve use of randomization. (E) surveys can make use of stratification.

(A) surveys are generally cheaper to conduct.

85) In the town of Lakeville, the number of cell phones in a household is a random variable W with the following probability distribution: Value w_i 0 1 2 3 4 5 Probability p_i 0.1 0.1 0.25 0.3 0.2 0.05 The standard deviation of the number of cell phones in a randomly selected house is (A)1.32 (B) 1.7475 (C) 2.5 (D) 0.09 (E) 2.9575

(A)1.32

43) If P(A)=.25 and P(B)=.34, what is P(A∪B) if A and B are independent? (A) .085 (B) .505 (C) .590 (D) .675 (E) There is insufficient information to answer this question.

(B) .505

56) Molly earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Molly? (Assume that test scores are normally distributed.) (A) 0.10 (B) 0.18 (C) 0.50 (D) 0.82 (E) 0.90

(B) 0.18

Questions 40 - 42 refer to this table: This two-way table gives frequencies of the combined simple events of color and size of marbles in a bag Blue Yellow White Black Total Small 27 34 16 10 87 Medium 7 19 53 13 92 Large 3 0 11 42 56 Total 37 53 80 65 235 42) Find the probability of a randomly drawn marble being large, given that the marble is black. (A) 0.35 (B) 0.65 (C) 0.22 (D) 0.20 (E) 0.80

(B) 0.65

51) It is estimated that 20 percent of all drivers do not signal when changing lanes. In a random sample of four drivers, what is probability that at least one doesn't signal when changing lanes? (A) 1-〖(.2)〗^4 (B) 1-〖(.8)〗^4 (C) 4(.2)〖(.8)〗^3 (D) 4(.2)^3 (.8) (E) 4(.2)^3 (.8)+6〖(.2)〗^2 〖(.8)〗^2+4(.2) (.8)^3+〖(.8)〗^4

(B) 1-〖(.8)〗^4

68) As part of a study on the relationship between the use of tanning booths and the occurrence of skin cancer, researchers reviewed the medical records of 1,436 people. The table below summarizes tanning booth use for people in the study who did and did not have skin cancer. Used Tanning Not Use Tanning Total Skin cancer 190 706 896 No skin cancer 75 465 540 Total 265 1,171 1,436 Of the people in the study who had skin cancer, what fraction used a tanning booth? (A) 190/265 (B) 190/896 (C) 190/1,436 (D) 265/1,436 (E) 896/1,436

(B) 190/896

74) The scores on a real estate licensing examination given in a particular state are normally distributed with a standard deviation of 70. What is the mean test score if 25% of the applicants scored above 475? (A) 416 (B) 428 (C) 468 (D) 522 (E) There is not enough information to answer this question.

(B) 428

22) Research indicates that the standard deviation of typical body temperate is 0.4 degrees Celsius (C). Which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where F=9/5 C+32? (A) 9/5 (0.4)+32 (B) 9/5(0.4) (C) 9/5 〖(0.4)〗^2 (D) (9/5)^2 (0.4) (E) (9/5)^2 〖(0.4)〗^2

(B) 9/5(0.4)

77) Assume X and Y are events in the same sample space. If P(X) = 0.30 and P(Y) = 0.75 then which of the following inequalities must be true? I. P(X ∩Y)≥0.05 II. P(X ∩Y)≥0.35 III. P(X ∩Y)≤0.30 (A) I and II (B) I and III (C) II and III (D) II only (E) I, II, III

(B) I and III

49) Staff members of a high school newspaper want to obtain an estimate of the average number of years teachers in the state have been teaching. At an educational conference attended by many teachers in the state, the staff members randomly selected 50 conference attendees and asked the attendees how long they have been teaching. Which of the following describes the sample and the population to which it would be most reasonable for the staff members to generalize the results? (A) The sample is the 50 conference attendees, and the population is all teachers in the state. (B) The sample is the 50 conference attendees, and the population is all the conference attendees. (C) The sample is all conference attendees, and the population is all teachers in the state. (D) The sample is all conference attendees, and the population is the 50 conference attendees. (E) The sample is the average number of years that all conference attendees have taught, and the population is all conference attendees.

(B) The sample is the 50 conference attendees, and the population is all the conference attendees.

61) The number of hybrid cars a dealer sells weekly has the following probability distribution: Number of hybrids 0 1 2 3 4 5 Probability .32 .28 .15 .11 .08 .06 The dealer purchases the cars for $21,000 and sells them for $24,500. What is the expected weekly profit from selling hybrid cars? (A) $2,380 (B) $3,500 (C) $5,355 (D) $8,109 (E) $37,485

(C) $5,355

19) A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. •20% of all tropical storms will originate in the Atlantic Ocean, of which 20% will be classified as major. •30% of all tropical storms will originate in the eastern Pacific Ocean, of which 15% will be classified as major. •50% of all tropical storms will originate in the western Pacific Ocean, of which 25% will be classified as major. Based on the meteorologist's estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major? (A) 0.045 (B) 0.125 (C) 0.170 (D) 0.400 (E) 0.960

(C) 0.170

84) A marketing survey complied data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, the X has the following probability distribution: X 0 1 2 3 4 5 P(X) 0.24 0.37 0.20 0.11 0.05 0.03 Using the problem above, what is the expected value of the number of cars in a randomly selected household? (A) 2.5 (B) 0.1667 (C) 1.45 (D) 1 (E) Cannot be determined

(C) 1.45

63) Ms. Fisher wants to compare the effect of a new fertilizer on that of three older fertilizers - X, Y, and Z - on the growth of vegetables typically grown in small gardens. Two hundred green bean seedlings were individually planted in identical pots and randomly assigned to one of four groups of 50 each. Seedlings in one group were given the new fertilizer, and the three remaining groups of seedlings were given fertilizers X, Y, or Z, respectively. At the end of four weeks, all seedlings were dried and weighed. Ms. Fisher found that the mean weight of the seedlings in the group given the new fertilizer were significantly greater than the mean weights of seedlings in the other three groups. The scientists concluded that the new fertilizer was more effective than the other fertilizers for all vegetables. Why is Ms. Fisher's conclusion not appropriate? (A) The study was observational, so cause and effect cannot be concluded. (B) The study was observational, so no replication was used in the study. (C) The experiment only included green beans, so the results cannot be generalized to all vegetables. (D) The experiment did not group the seedlings into blocks by the variety of beans. (E) The experiment lacked a control group that did not use any fertilizer.

(C) The experiment only included green beans, so the results cannot be generalized to all vegetables.

67) If the standard deviation of a set is 0, you can conclude (A) that there is no relationship between the observations (B) that the average value is 0 (C) that all observations are the same value (D) that a mistake in arithmetic has been made (E) none of the above

(C) that all observations are the same value

87) The faces of a four-sided fair die are numbered 1 through 4, respectively. For a certain game, the die is tossed and the number that lands facedown is recorded. the table below summaries the points a player earns for the number that lands facedown. Number landing facedown 1 2 3 4 Points 0 1 0 2 Consider two independent tosses of the die. Let the random variable S represent the sum of the points earned from the two tosses. Which table represents the probability distribution of S? (A) S 0 1 2 Probability 0.5 0.25 0.25 (B) S 0 2 4 Probability 0.5 0.25 0.25 (C) S 0 2 4 Probability 0.25 0.5 0.25 (D) S 0 1 2 3 4 Probability 0.25 0.25 0.3125 0.125 0.0625 (E) S 0 1 2 3 4 Probability 0.0625 0.25 0.375 0.25 0.0625

(D) S 0 1 2 3 4 Probability 0.25 0.25 0.3125 0.125 0.0625

55) The number of tickets purchased by a customer for the Ice Hogs game at BMO Harris Bank center can be considered a random variable. The table below show the relative frequency distribution for the number of tickets purchased by a customer. Number of tickets purchased 1 2 3 4 5 Relative Frequency 0.20 0.45 0.10 0.20 0.05 Suppose each ticker for the game cost $12. Based on the distribution shown, what is the mean cost per customer for the game? (A) $2.45 (B) $2.75 (C) $24.50 (D) $29.40 (E) $36.00

(D) $29.40

83) A marketing survey complied data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, the X has the following probability distribution: X 0 1 2 3 4 5 P(X) 0.24 0.37 0.20 0.11 0.05 0.03 What is the probability that a randomly chosen household has at least two cars? (A) 0.19 (B) 0.20 (C) 0.29 (D) 0.39 (E) 0.61

(D) 0.39

59) The SAT math scores for applicants to a particular engineering school are normally distributed with a mean of 680 and a standard deviation of 35. Suppose that only applicants with scores above 700 are considered for admission. What percentage of the applicants considered have scores below 750? (A) 2.3 percent (B) 26.1 percent (C) 71.6 percent (D) 92.0 percent (E) 97.7 percent

(D) 92.0 percent

3) What are the categorical variables in your survey? (A) Family size, dad's occupation, whether mom works, and kind of pets (B) Dad's occupation, whether mom works, and kind of pets (C) Grade of youngest child, dad's occupation, whether mom works, and kind of pets (D) Everything but average annual income and family size (E) Everything but average annual income

(D) Everything but average annual income and family size

11) 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

(D) I, III, and IV

72) Halle takes three standardized tests. She scores 600 on all three. Using standardized scores (z-scores), rank her performance on the three tests from best to worst if the means and standard deviations of the tests are as follows: Mean Standard Deviation Test I 500 80 Test II 470 120 Test III 560 30 (A) I, II, and III (B) III, II, and I (C) I, III, and II (D) III, I, and II (E) II, I, and III

(D) III, I, and II

39) A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she's been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the best way for her to carry out the randomization for this study? (A) Use a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flip a coin to decide which pavement to use on which member of the pair. (B) Subjectively divide the 40 roadways into 20 pairs (making the roadways within each pair as different as possible) and then, for each pair, flip a coin to decide which pavement to use on which member of the pair. (C) Use a table of random digits to divide the 40 roadways into two groups of twenty, and then use the table of random digits a second time to decide which pavement to use on which group. (D) Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement. (E) Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin once to decide which pavement is put on the first half-mile of all the roadways.

(D) Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement.

44) An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand. Is this an example of a simple random sample? (A) Yes, because each buyer in the sample was randomly sampled. (B) Yes, because each buyer in the sample had an equal chance of being sampled. C) Yes, because car buyers of every brand were equally represented in the sample. (D) No, because every possible 400-buyer sample did not have an equal chance of being chosen. (E) No, because the population consisted of purchasers of four different brands of car.

(D) No, because every possible 400-buyer sample did not have an equal chance of being chosen.

2) Which of the variables you collect are continuous data? (A) Average annual income and phone number (B) Only family size (C) Grade of youngest child and average annual income (D) Only average annual income

(D) Only average annual income

9) 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

(D) P(D or E) = 0.72

34) A bank wishes to survey its customers. The decision is made to randomly pick ten customers who just have checking accounts, ten customers who just have savings accounts, and ten customers who have both checking and savings accounts. This procedure is an example of which type of sampling? (A) Cluster (B) Convenience (C) Simple random (D) Stratified (E) Systematic

(D) Stratified

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. 6) 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

(D) z = -0.4

29) A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test? (A) 82 (B) 88 (C) 100 (D) 112 (E) 118

(E) 118

28) Suppose the scores on an exam have a mean of 75 with a standard deviation of 8. If one student has a test result with a z-score of -1.5, and a second student has a test result with a z-score of 2.0, how many points higher was the second student's result than that of the first? (A) 3.5 (B) 4 (C) 12 (D) 16 (E) 28

(E) 28

100) The following numbers appear in a table of random digits: 38683 50279 38224 09844 13578 12708 24684 A scientist will be measuring the total amount of leaf litter in a random sample (n = 5) of forest sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02, ... , 45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following represents her sample? (A) 38, 25, 02, 38. 22 (B) 38, 68, 35, 02, 22 (C) 38, 35, 27, 28, 08 (D) 38, 65, 35, 02, 79 (E) 38, 35, 02, 22, 40

(E) 38, 35, 02, 22, 40

46) Which of the following are true? I. Two events are mutually exclusive if they can't both occur at the same time. II. Two events are independent if they have the same probability. III. An event and its complement have probabilities that always add to 1. (A) I only (B) II only (C) III only (D) I and II only (E) I and III only

(E) I and III only

97) Which of the following statements is true for two events, each with probability greater than 0? (A) If the events are mutually exclusive, they must be independent. (B) If the events are independent, they must be mutually exclusive. (C) If the events are not mutually exclusive, they must be independent. (D) If the events are not independent, they must be mutually exclusive. (E) If the events are mutually exclusive, they cannot be independent.

(E) If the events are mutually exclusive, they cannot be independent.

1) A scientist recorded the duration of the eruption of the Old Faithful geyser in Yellowstone National Park that occurred during a one-month time period. The histogram below shows the distribution of the duration, in seconds, of the eruptions. Based on the histogram, which of the following is the best description of the distribution? (A) The distribution is uniform, is centered at about 200 seconds, and has a range of at most 250 seconds. (B) The distribution is skewed to the left, is centered at about 125 seconds, and has a range of at most 250 seconds. (C) The distribution is skewed to the right, is centered at about 26 0seconds, and has a range of at most 250 seconds. (D) The distribution displays two clusters, has a range of at most 200 seconds, and includes outliers below 75 seconds and above 325 seconds. (E) The distribution displays two clusters, with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.

(E) The distribution displays two clusters, with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.

24) An AP Statistics teacher grades using z-scores. On the second major exam of the marking period, a student receives a grade with a z-score of -1.3. What is the correct interpretation of this grade? (A) The student's grade went down 1.3 points from the first exam. (B) The student's grade went down 1.3 points more than the average grade went down from the first exam. (C) The student scored 1.3 standard deviations lower on the second exam than on the first. (D) The student scored 1.3 standard deviations lower on the second exam than the class average on the first exam. (E) The student scored 1.3 standard deviations lower on the second exam than the class average on the second exam.

(E) The student scored 1.3 standard deviations lower on the second exam than the class average on the second exam.

26) Given two independent random variables, X with mean 12.3 and standard deviation 0.5 and Y with mean 9.1 and standard deviation 0.3, which of the following is a true statement? (A) The mean of X-Y is 21.4 (B) The median of X-Y is 3.2 (C) The range of X-Y is 21.4 (D) The standard deviation of X-Y is 0.8 (E) The variance of X-Y is 0.34

(E) The variance of X-Y is 0.34

103) Suppose the probability that a softball player gets a hit in any single at-bat is .300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other at bats, what is the probability that she will not get a hit until her fourth time at bat in a game? (A) (■(4@3)) 〖(.3)〗^1 〖(.7)〗^3 (B) (■(4@3)) 〖(.3)〗^3 〖(.7)〗^1 (C) (■(4@1)) 〖(.3)〗^3 〖(.7)〗^1 (D) 〖(.3)〗^3 〖(.7)〗^1 (E) 〖(.3)〗^1 〖(.7)〗^3

(E) 〖(.3)〗^1 〖(.7)〗^3