AP Stats Test Answers

9. A rock concert producer has scheduled an outdoor concert. If it is warm that day, she expects to make a $20,000 profit. If it is cool that day, she expects to make a $5000 profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based upon historical records, the weather office has estimated the chances of a warm day to be 0.60; the chances of a cool day to be 0.25. What is the producer's expected profit

$11,450

92. Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Noraml with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than

$255

83. Mr. Yates picked up a dozen items in the grocery store with a mean cost of $3.25. Then he added an apple pie for $6.50. The new mean for all 13 items is

$3.50

77. Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

(10/3)(1/8)^3(7/8)^7

23. In some courses (but certainly not in an intro stats course!), students are graded on a "Normal curve." For example, students within +/- 0.5 standard deviations of the mean receive a C; between 0.5 and 1.0 standard deviations above the mean receive a C+; between 1.0 and 1.5 standard deviations above the mean receive a B-; between 1.5 and 2.0 standard deviations above the mean receive a B, etc. The class average on an exam was 60 with a standard deviation of 10. The bounds for a B- grade and the percent of students who will receive a B- grade if the marks are actually Normally distributed are

(70,75), 9.19%

75. The variance of sum of two random variables X and Y is

(s(x)2 + (s(y)2, but only if X and Y are independent

33. The incomes in a certain large population of college teachers have a normal distribution with mean $60,000 and standard deviation $5000. Four teachers are selected at random from the population to serve on a salary review committee. What is the probability that their average salary exceeds $65,000

0.0228

55. Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (We will ignore the small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death was due to diabetes is about

0.030

78. Let the random variable X represent the weight of male black bears before they begin hibernation. Research has shown that X is approximately Normallly distributed with a mean of 250 pounds and a standard deviation of 50 pounds. What is P(x>325 pounds)

0.0668.

35. There are 10 red marbles and 8 green marbles in a jar. If you take three marbles from the jar (without replacement), the probability that they are all red is

0.147

85. You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. What is the probability that both marbles are red

0.1551

61. Use Scenario 5-13. You select one student from this group at random. If the student says he is a junior, what is the probability that he walks to school

0.160

72. Jun and Deron are applying for summer jobs at a local restaurant. After interviewing them, the restaurant owner says, "The probability that I hire Jun is 0.7, and the probability that I hire Deron is 0.4. The probability that I hire at least one of you in 0.9." What is the probability that both Jun and Deron get hired

0.2

91. 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)

0.2119

70. If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is 0.11. Given the nature of lotteries, the probability of winning is independent from month to month. If you buy one ticket each month for five months, what is the probability that you will win at least one prize

0.44

17. People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least one of them is a universal donor

0.526

36. Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person crime. Then the probability of observing no positive readings if all suspects plead innocent and are telling the truth is

0.591

43. If PA=0.24 and PB=0.52 and A and B are independent, what is P(A or B)

0.6352

56. The security system in a house has two units that set off an alarm when motion is detected. Neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. Suppose that for motion in a certain location, the probability that detector A goes off and detector B does not go off is 0.25, and the probability that A does not go off is 0.35. What is the probability that B goes off

0.75

59. The probability that a randomly selected household has at least 2 cell phones is

0.80.

21. A college basketball player makes 80% of her free throws. At the end of the game, her team is losing by two points. She is fouled attempting a three-point shot and is awarded three free throws. Assuming free throw attempts are independent, what is the probability that she makes at least two of her free throws

0.896

51. Here are the IQ test scores of 10 randomly chosen fifth-grade students-145,139,126,122,125,130,96,110,118,118. To make a stemplot of these scores, you would use as stems

09,10,11,12,13, and 14.

4. The cumulative relative frequency graph below shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. The interquartile range for this distribution is approximately

1.2 centimeters

68. A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the number of service calls in a month y at each location. Summary calculations give x-bar=8.4, s(x)=2.1, y-bar=14.2, s(y)=3.8, and r=0.86. What is the slope of the least-squares regression line of number of service calls on number of copies

1.56

14. Use the information in the previous problem. About what percentage of men are over 70.5 inches tall

16

53. Use scenario 6-13. Which of the following is the approximate standard deviation of X

19

44. The distribution of the heights of students in a larger class is roughly Normal. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to

3

54. Kitchen appliances don't last forever. The lifespan of all microwave ovens sold in the United States is approximately Normally distributed with a mean of 9 years and a standard deviation of 2.5 years. What percentage of the ovens last more than 10 years

34.5%

52. Use scenario 6-13. Which of the following is the mean of X

600

5. The heights of American men aged 18 to 24 are approximately normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range

63 inches to 73 inches

96. In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines

74%

46. A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of adult women in one of the countries. Country A-92,110,120,160,240. About what percent of Country A women weight between 110 and 240 pounds

75%

97. Use Scenario 3-15. Joseph is 22.5 months old. What is his predicted height

79.11

45. If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the sale but also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, the standard deviation is 15, and a histogram of the demand is approximately Normal. The manager is willing to accept a 2.5% chance that a CD will be sold out. About how many CDs should the manager order for the sale

875

29. The five-number summary for scores on a statistics test is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many scored between 35 and 61

95

41. In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y=10+0.9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam

95.5

81. A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear in these 1996 additional tosses

998

13. To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is

A matched pairs experiment

39. Select a random integer from -100 to 100. Which of the following pairs of events are mutually exclusive (disjoint)

A-the number is above 50 and B-the number is less than 20

16. Which of these variables is least likely to have a normal distribution

Annual income for all 150 employees at a local high school

2. Which statements below about the least-squares regression line are correct?I. Switching the explanatory and response variables will not change the least-squares regression line.II. The slope of the line is very sensitive to outliers with large residuals.III. A value of r2 close to 1 does not guarantee that the relationship between the variables is linear

Both II and III are correct

50. Which of the following statements are true? I. The area under the Normal curve is always 1, regardless of the mean and standard deviation. II. The mean is always equal to the median for any Normal distribution. III. The interquartile range for any Normal curve extends from mean-S(x) to mean+s(x)

I and II

42. Which of the following properties is true for all Normal density curves? I. They are symmetric II. The curve reaches its peak at the meanIII. 95% percent of the area under the curve is within one standard deviation of the mean

I and II only

95. For the histogram below, what is the proper ordering of the mean and median? Note that the graph is not numerically precise—only the relative points are important

I is the mean and II is the median

47. Which of the following statements is/are true when taking an SRS from a large population? I. The sampling distribution of x has standard deviation s(x)/sq root of , even if the population is not Normally distributed. II. The sampling distribution of x is Normal if the population has a Normal distribution. III. When n is large, the sampling distribution of x is approximately normal even if the population is not Normally distributed

I,II, and III

49.A randomly chosen subject arrives for a study of exercise and fitness. Consider these statements. I. After 10 minutes on an exercise bicycle, you ask the subject to rate his or her effort on the rate of perceived exertion (RPE) scale. RPE ranges in whole-number steps from 6 (no exertion at all) to 20 (maximum exertion). II. You measure VO2, the maximum volume of oxygen consumed per minute during exercise. VO2 is generally between 2.5 liters per minute and 6 liters per minute. III. You measure the maximum heart rate (beats per minute). The statements that describe a discrete random variable are

I,III.

48. In order to use the formula s(X)=s(x)/sq. root of n to calculate the standard deviation of the sampling distribution of the sample mean, which of the following conditions must be met? I. N>30 II. The population's distribution is approximately Normal. III. The sample size is less than 10% of the population size

III only

79. The mean speed of vehicles in the "cars only" lane of the New Jersey turnpike is 68 miles per hour. The mean speed of vehicles in the "any vehicle" lane is 64 miles per hour. What must be true about the mean speed of all vehicles on the turnpike, assuming these are the only types of lanes

It could be any number between 64 and 68 miles per hour

57. According to a 1990 census, those states with an above-average number of people X, who fail to complete high school tend to have an above average number of infant deaths, Y. In other words, there is a positive association between X and Y. The most plausible explanation for this is

Lurking variables are probably present. For example, states with large populations may have both larger numbers of people who don't complete high school and more infant deaths.

12. You take a sample of size 25 from a very large population in which the true proportion is p=0.1, thus violating the condition that np>10 and n(1-p)>10. Which statement below best describes what you know about the sampling distribution of p

Mean=0.1; S(x)=(0.1*0.9)/25)^.5; the distribution is not approximately Normal

15. A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $5.00 per day to maintain the machine and rent the space for it. What are the mean and standard deviation for Y=the profit he earns from this machine in a randomly-selected week

Mean=26.25, standard deviation=$1.75

86. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then

P(A or B)=1.0

6. The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is

Skewed to the right, with mean 0 and standard deviation 1

3. A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y=1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements is not necessarily true

The actual relationship between salary raises and performance rating is linear

11. The graph below is a normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true

The distribution is skewed right

8. The weights of the male and female students in a class are summarized in the following boxplot. Which of the following is NOT correct

The male students have less variability than the female students

20. When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million); 5, 7, 12, bdl, 10, 8, bdl, 20, 6

The median lead level in the water is 7 ppm

24. Which of the following random variables is geometric

The number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7

94. A researcher reports that the participants in his study lost a mean of 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct

The report gives only the mean. This does not imply that all participants in the study lost 10.4 pounds or even lost weight. Your friend's experience does not necessarily contradict the study results.

7. What is the distribution of values taken by a statistic in all possible samples of the same size from the same population called

The sampling distribution of the statistic

98. The pie chart describes the distribution of state tree types for the 50 states in the United States. The category "Other" include all trees that are the state tree for two or fewer states. Which of the following conclusions can we draw from the chart

There are 10 states that have designated pine as their state tree

10. A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting

Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected

93. At a school with 600 students, 25% of them walk to school each day. If we choose a random sample of 40 students from the school, is it appropriate to model the number of students in our sample who walk to school with a binomial distribution where n=40 and p=0.25

Yes, because the sample size is less than 10% of the population size

37. You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked her attitude toward the product. You think there may be large differences between women who are employed outside the home and those who are not. Because of these differences, you should use

a block design

89. A stratified random sample addresses the same issues as which of the following experimental designs

a block design

73. A nutritionist wants to study the effect of storage time (6,12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of three storage times. The treatment, experimental unit, and response are respectively

a specific storage time, a fruit pack, amount of vitamin C

66. Which of the following is a true statement

an important difference between binomial and geometric random variables is that there is a fixed number of in a binomial setting, and the number of trials varies in a geometric setting

80. If your score on the test is at the 60th percentile, you know that your score lies

between the median and the third quartile

76. We say that the design of a study is biased if which of the following is true

certain outcomes are systematically favored

30. A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maples trees in a large forest. There are too many trees to list them all and take an SRS, so he divides the forest into several hundred 10 meter by 10 meter plots, selects 25 plots at random, and measures the diameter of every single Sugar Maple in each one. This is an example of a

cluster sample

38. Control groups are used in experiments in order to

control the effects of outside variables on the outcome

60. A double-blind experiment was conducted to evaluate the effectiveness of the Salk polio vaccine. The purpose of keeping the diagnosing physicians ignorant of the treatment status of the experimental subjects was to

eliminate the possible source of bias

64. Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this study

gas mileage is a response variable, and you expect to find a negative association

90. A recent survey by a large-circulation Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." The main problem with using these results to draw conclusions about the general public's perception is

lack of random selection

74. 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 the 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

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

31. The best statistic for estimating a parameter has which of the following characteristics

low bias, low variability

100. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is

mean=2, s(x)=1.265

26. The 16th percentile of a Normally distributed variable has a value of 25 and the 97.5th percentile has a value of 40. Which of the following is the best estimate of the mean and standard deviation of the variable

mean=30, s(x)=5

18. A student investigating study habits asks a simple random sample of 16 students at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are mean=45 minutes and s(x)=15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student's sample

mean=45, s(x)=3.75, shape of distribution unknown

71. If A=result of a single roll of a six-sided die and B=result of a single roll of an 8-sided die, then meanA=3.5, S(a)=1.71, meanB=4.5, and S(b)=2.29. If D=the difference B-A, then which of the following is true

meanD=1, S(d)=sq root(1.71)²+(2.29)²

34. You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. "Least-squares" refers to

minimizing the sum of the squares of the residuals

32. An experiment to measure the effect of giving growth hormones to girls affected by Turner's Syndrome was carried out recently in Vancouver. All 34 girls were given the growth hormone and their heights were measured at the time the hormone was given and again one year later. No measurements were made on their final adult heights. Which of the following is not a problem with this experiment

nonresponse bias

22. A small company estimating its photocopying expenses finds that the mean number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation

on average, the number of copies made each day was about 24 copies per day away from the mean, 258

67. The reason that blocking (in a randomized block design) is sometimes used in experimentations is to

reduce variability arising from random assignment

69. The central limit theorem refers to which of the following characteristics of the sampling distribution of the sample mean

regardless of the shape of the population's distribution, the sampling distribution of the sample mean from sufficiently large samples will be approximately normally distributed

40. Mr. Nerdly asked the students in his AP Statistics class to report their overall grade point averages and their SAT Math scores. The scatterplot below provides information about his students' data. The dark line is the least-squares regression line for the data, and its equation is y=410.54+67.3x. Which of the following about the circled point is false

removing the student's data point would increase the slope of the least-squares line

63. Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll conducted for the Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. Which of the following terms describes the number 92%

statistic

1. In an experiment, an observed effect so large that it would rarely occur by chance is called

statistically significant

19. A public opinion poll in Ohio wants to determine whether or not registered voters in the state approved of a measure to ban smoking in all public areas. They select a simple random sample of fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of a

stratified random sample

99. A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000 undergraduate students and a separate SRS of 100 of the 5,000 graduate students. This kind of sample is called a

stratified random sample

87. A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual tell you about the linear model

the curved pattern in the residual plot suggests that the linear model is not appropriate

28. The sampling distribution of a statistic is

the distribution of values taken by a statistic in all possible samples of the same sample size from the same population

62. Use Scenario 5-13. You select one student from the group at random. Which of the following statements is true about the events "Typically walks to school" and Junior

the events are not mutually exclusive but they are independent

65. You have data for many families on the parents' income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot

the explanatory variable is parents' income, and you expect to see a positive association

27. If a distribution is skewed to the right, which of the following is true

the mean must not be greater than the median

25. A small company that prints custom T-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which of the following describes how the company's mean and median salaries would change

the mean would increase by $5,000 and the median would not change

58. The probability of any outcome of a random phenomena is

the proportion of times the outcome occurs in a very long series of repetitions

84. If a statistic is used to estimate a parameter is such that the mean of the sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be

unbiased

82. Which of the following is a method for improving the accuracy of a sample

use larger sample sizes

88. An agricultural economist says that the correlation between corn prices and soybean prices is r=0.7. This means that

when corn prices are above average, soybean prices also tend to be above average