AP Probability and Statistics (Stranquist): Final Exam Questions 91-108

92. Suppose study participants are asked two questions. Based on a large number of participants, the probability distribution for the responses to Question 1 and 2 is given below. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with a µ= $360 and σ= $50. What is P(X > $400)? a) 0.2119 b) 0.2881 c) 0.5319 d) 0.7881 e) 0.8450

a) 0.2119

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 situation? a) Assign "0, 1 , 2" as watching the shopping channel at least once a week and "3, 4, 5, 6, 7, 8, 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, 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, 0" as not watching d) Assign "0" as watching the shopping channel at least once a week and "1, 2, 3 , 4, 5" as not watching; ignoring digits "6, 7, 8, 9" e) Assign "3" as watching the shopping channel at least once a week and "0, 1, 2, 4, 5, 6, 7, 8, 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, 9" as not watching

101. The effect of removing the right-most point (bear the positive x-axis) in the scatterplot shown would be: a) The slope of the LSRL will increase; r will decrease b) The slope of the LSRL will increase; r will decrease c) The slope of the LSRL will decrease; r will increase d) The slope of the LSRL will decrease; r will decrease e) no change

a) The slope of the LSRL will increase; r will decrease

94. Given a set of ordered pairs (x, y) so that sx = 0.75 , sy = 1.6 , r = 0.55. What is the slope of the least-squares regression line? a) 1.82 b) 1.17 c) 2.18 d) 0.26 e) 0.78

b) 1.17

99. A set of data relates the amount of annual salary raise and the performance rating. The least squares regression equation y= 2000x + 1400 where y is the estimated raise and x is the performance rating. Which of the following statements is not correct? a) For each increase of one point in performance rating, the raise will increase on average by $2000 b) This equation produces predicted raises with an average error of 0 c) A rating of 0 will yield a predicted raise if $1400 d) The correlation for the data is positive e) All of the above are true

b) This equation produces predicted raises with an average error of 0

108. A large bakery has many different products for sale. Suppose that 70% of all customers of the bakery ordered 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? a) 20% b) 24% c) 40% d) 48% e) 60%

c) 40%

91. Suppose study participants are asked two questions. Based on a large number of participants, the probability distribution for the responses to Question 1 and 2 is given below. For one participant, let A = Question 1 is answered correctly and B = Question 2 is answered correctly. Which of the following must be true? a) A and B are independent because each question is correct with probability 0.50, and the probability that both questions are answered correctly is (0.5)(0.5)= 0.25 b) A and B are not independent because the probability in each cell is not 0.25 c) A and B are not independent because (0.33)(0.45) does not equal 0.25 d) A and B are not independent because one participant's answers do not affect another participant's answers e) There is not enough information provided to determine whether A and B are independent

c) A and B are not independent because (0.33)(0.45) does not equal 0.25

98. The SC Electric Company has bud in 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 - 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 as µ= 75 and the standard deviation was σ=10. On the second exam, the class mean was µ=70 and the standard deviation was σ=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 exams is not given

c) She scored about equally well on both exams

102. A scatterplot if student heights, in inches, versus corresponding arm span length, in inches, is shown below One if the points in the graph is labeled A. If the point labeled A is removed which of the following would be true? a) The slope of the least squares regression line is unchanged and the correlation coefficient increases. b) The slope of the least squares regression line is unchanged and the correlation coefficient decreases c) The slope of the least squares regression line increases and the correlation coefficient increases d) The slope of the least squares regression line increases and the correlation coefficient decreases e). The slope of the least squares regression line decreases and the correlation coefficient increases

c) The slope of the least squares regression line increases and the correlation coefficient increases

103. Suppose the probability that a softball player gets him in any single at-bat is .300. Assuming that her chance of getting a hit in a particular time at bat is independent of her other at baths, 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

106. What is the size of a typical prediction error if this regression line? a) 95.6 b) 0.978 c) 23.983 d) 1.947 e) 30.16

e) 30.16

100. The following numbers appear in a table of random digits: 38683, 50279, 38224, 09844, 13578, 12708, 24684 A scientist rust 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 bigots 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

104. A linear regression was performed using five following data points A(1, 11) B(5, 2) C(3, 7) D(7, 1) E(9, -2) a The residual for which of the five points has the largest absolute value? a) A b) B c) C d) D e) E

e) E

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

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 f car accident 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