A.P. Statistics Review for Fall Final Exam - Multiple Choice Questions

36) Which of the following statements is incorrect?

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

30) An advantage to using surveys as opposed to experiments is that

(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

(A)1.32

43) If P(A)=.25 and P(B)=.34, what is P(A∪B) if A and B are independent?

(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.)

(B) 0.18

14) In which of the following histograms is the mean less than the median?

(C)

50) Suppose P(X)=.25 and P(Y)=.40. If P(X│Y)=.20, what is P(Y|X)?

(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?

(C) 0.4412

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?

(C) 0.50

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

(C) 3000

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?

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

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?

(C) Simple random

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?

(C) The distribution is skewed right

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

(D) 19.99 to 20.01 millimeters

11) Which of the following can outliers affect significantly? I. Mean II. Median III. Standard deviation IV. Range V. Interquartile range

(D) I, III, and IV

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?

(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.

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 a cd s follows:

(E) II, I, and III

97) Which of the following statements is true for two events, each with probability greater than 0?

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

93) Which of the following random variables has a distribution which most closely resembles a normal distribution?

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

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? (C) 0.170

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

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? (D) $29.40

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? (D) 90

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

(A)

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

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

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

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

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

8) Why is the IQR considered to be a resistant statistic?

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

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.

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.

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.

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.

37) A critical difference between experiments and observational studies is

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

To which of the histograms below can the boxplot correspond?

(B)

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.

(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?

(B) 1-〖(.8)〗^4

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

(B) 16.5 years and 38.1 years

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.

(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?

(B) 428

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?

(B) 5.00

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?

(B) 9/5(0.4)

70) Control groups are used in experiments in order to ...

(B) Control the subjects of a study so as to insure all participate equally.

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?

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

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:

(B) independent, but not mutually exclusive.

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

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

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?

(C) $5,355

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?

(C) 0.526

84) Using the problem above, what is the expected value of the number of cars in a randomly selected household?

(C) 1.45

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?

(C) 30

108) A large bakery has many different products for sale. Suppose that 70% of all customers of the bakery order donuts. 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?

(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?

(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?

(C) 7.00 pounds

12) Given these parallel boxplots, which of the following is incorrect?

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

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?

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

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

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

67) If the standard deviation of a set is 0, you can conclude

(C) that all observations are the same value

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?

(D) 0.673

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?

(D) 25th percentile

71) A sample of production records for an automobile manufacturer shows the following figures for production per shift:

(D) 50.00

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?

(D) 92.0 percent

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?

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

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?

(D) At least 1

You want to know something about your neighbors, so you give them a survey. The survey collects the following data about each family on your block: family size, the kind of pets they have, the grade of the youngest child in the family, the family's average annual income over the last five years, what the dad does for a living, whether the mom works, and their phone number. Each kind of data you collect about a family is a variable. 3) What are the categorical variables in your survey?

(D) Everything but average annual income and family size

13) Which of the following is true about the areas described under the normal curve?

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

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?

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

You want to know something about your neighbors, so you give them a survey. The survey collects the following data about each family on your block: family size, the kind of pets they have, the grade of the youngest child in the family, the family's average annual income over the last five years, what the dad does for a living, whether the mom works, and their phone number. Each kind of data you collect about a family is a variable. 2) Which of the variables you collect are continuous data?

(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?

(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?

(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?

(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?

(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?

(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?

(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.

(E) I and III only

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.

(E) I, II, and III

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.

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

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 shoes the distribution of the curation, in seconds, of the eruptions. Based on the histogram, which of the following is the best description of the distribution?

(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?

(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?

(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?

(E) 〖(.3)〗^1 〖(.7)〗^3

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 (B) I and III

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?

If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B? (C) Event A and event B are not mutually exclusive and are independent.

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: (B) 0.15

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? (D) 0.39

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? (D) 0.89

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? (E) E