Download Ch 7 and 8 questions

Ch 7 and 8 Review questions
1. Of the coral reef species on the Great Barrier Reef off Australia, 73% are poisonous. If a tourist boat
taking divers to different points off the reef en- counters an average of 25 coral reef species, what are the
mean and standard deviation for the expected number of poisonous species seen?
(A)  x = 6.75,  x = 4.93
(B)  x = 18.25,  x = 2.22
(C)  x == 18.25,  x = 4.93
(D)  x = 18.25,  x = 8.88
(E) None of the above gives a set of correct answers.
2. According to a CBS/New York Times poll taken in 1992, 15% of the public
have responded to a telephone call-in poll. In a random group of five people,
what is the probability that exactly two have responded to a call-in poll?
(A) .138
(B) .165
(C) .300
(D) .835
(E) .973
3. Alan Dershowitz, one of 0.1. Simpson's lawyers, has stated that only lout of every 1000 abusive
relationships ends in murder each year. If he is correct, and if there are approximately 1.5 million
abusive relationships in the United States, what is the expected value for the number of people who are
killed each year by an abusive partner?
(A) 1
(B) 500
(C) 1000
(D) 1500
(E) None of the above
4. A television game show has three payoffs with the following probabilities:
Payoff ($):
0
1000 10,000
Probability: .6
.3
.1
What are the mean and standard deviation for the payoff variable?
(A)  x = 1300,  x = 2934
(B)  x = 1300,  x = 8802
(C)  x = 3667,  x = 4497
(D)  x = 3667,  x = 5508
(E) None of the above gives a set of correct answers
5. An inspection procedure at a manufacturing plant involves picking three items at random and then
accepting the whole lot if at least two of the three items are in perfect condition. If in reality 90% of the
whole lot are perfect, what is the probability that the lot will be accepted?
(A) .600
(B) .667
(C) .729
(D) .810
(E) .972
6. At a warehouse sale 100 customers are invited to choose one of 100 identical boxes. Five boxes
contain $700 color television sets, 25 boxes contain $540 camcorders, and the remaining boxes contain
$260 cameras. What should a customer be willing to pay to participate in the sale?
(A) $260
(B) $352
(C) $500
(D) $540
(E) $699
7. There are two games involving flipping a coin. In the first game you win a prize if you can throw
between 40% and 60% heads. In the second game you win if you can throw more than 75% heads. For
each game would you rather flip the coin 50 times or 500 times?
(A) 50 times for each game
(B) 500 times for each game
(C) 50 times for the first game, and 500 for the second
(D) 500 times for the first game, and 50 for the second
(E) The outcomes of the games do not depend .on the number of flips
8. The average annual incomes of high school and college graduates in a Midwestern town are $21,000
and $35,000, respectively. If a company hires only personnel with at least a high school diploma and
20% of its employees have been through college, what is the mean income of the company employees?
(A) $23,800
(B) $27,110
(C) $28,000
(D) $32,200
(E) $56,000
9. An insurance company charges $800 annually for car insurance. The policy specifies that the
company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a
motorist having a minor accident during the year is .2, and of having a major accident, .05, how much
can the insurance company expect to make on a policy?
(A) $200
(B) $250
(C) $300
(D) $350
(E) $450
10. Which of the following are true statements?
I. By the law of large numbers, the mean of a random variable will get closer and closer to a specific
value.
II. The standard deviation of a random variable is never negative.
III. The standard' deviation of a random variable is 0 only if the random
variable takes a lone single value.
(A) I and II
(B) I and III
(C) II and III
(D) I, II, and III
(E) None of the above gives the complete set of true responses.
11. You can choose one of three boxes. Box A has four $5 bills and a single $100 bill, box B has 400 $5
bills and 100 $100 bills, and box C has 24 $1 bills. You can have all of box C or blindly pick one bill out
of either box A or box B. Which offers the greatest expected winning?
(A) Box A
(B) Box B
(C) Box C
(D) Either A or B, but not C
(E) All offer the same expected winning.
12. Companies proved to have violated pollution laws are being fined various amounts with the
following probabilities:
Fine ($):
1000
10,000
50,000
100,000
Probability:
.4
.3
.2
.1
What are the mean and standard deviation for the fine variable?
(A)  x = 40,250,  x = 39,118
(B)  x = 40,250,  x = 45,169
(C)  x = 23,400,  x = 31,350
(D)  x = 23,400,  x = 85,185
(E) None of the above gives a set of correct answers.
13. Mathematically speaking, casinos and life insurance companies make a profit because of
(A) their understanding of sampling error and sources of bias.
(B) their use of well-designed, well-conducted surveys and experiments.
(C) their use of simulation of probability distributions.
(D) the central limit theorem.
(E) the law of large numbers.
14. Suppose you are one of 7.5 million people who send in their name for a drawing with 1 top prize of
$1 million, 5 second-place prizes of $10,000, and 20 third-place prizes of $100. Is it worth paying 32
cents for to send in your name?
(A) Yes, because (1,000,000/.32) = 3,125,000, which is less than 7,500,000.
(B) No, because your expected winnings are only $0.14.
(C) Yes, because (7,500,000/(1+5+20)) = 288,462.
(D) No, because 1,052,000 < 7,500,000.
(E) Yes because (1,052,000/20) = 40,462.
15. You have a choice of three investments, the first of which gives you a 10% chance of making $1
million, otherwise you lose $25,000; the second of which gives you a 50% chance of making $500,000,
otherwise you lose $345,000; and the third of which gives you an 80% chance of making $50,000,
otherwise you make only $1,000. Assuming you will go bankrupt if you don't show a profit, which
option should you choose for the best chance of avoiding bankruptcy?
(A) First choice
(B) Second choice
(C) Third choice
(D) Either the first or the second choice
(E) All the choices give an equal chance of avoiding bankruptcy.
16. Can the function f(x) = ((x + 6)/24), for x = 1, 2, and 3, be the probability distribution for some
random variable?
(A) Yes
(B) No, because probabilities cannot be negative.
(C) No, because probabilities cannot be greater than 1.
(D) No, because the probabilities do not sum to 1.
(E) Not enough information is given to answer the question.
17. Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four couples
file for a divorce, what is the probability that exactly two will state incompatibility as the reason?
(A) .104
(B) .207
(C) .254
(D) .311
(E) 0423
18. Suppose we have a random variable X where the probability associated with the value k is
10 
  (.37) k ( .63) 10 k for k = 0, . . ., 10. What is the mean of X?
k
(A) 0.37
(B) 0.63
(C) 3.7
(D) 6.3
(E) None of the above
19. Suppose you toss a coin ten times and it comes up heads every time. Which of the following is a true
statement?
(A) By the law of large numbers, the next toss is more likely to be tails than another heads.
(B) By the properties of conditional probability, the next toss is more likely to be heads given that ten
tosses in a row have been heads.
(C) Coins actually do have memories, and thus what comes up on the next toss is influenced by the past
tosses.
(D) The law of large numbers tells how many tosses will be necessary before the percentages of heads
and tails are again in balance.
(E) The probability that the next toss will again be heads is .5.
20. Which of the following lead to binomia1.distributions?
I. An inspection procedure at an automobile manufacturing plant involves selecting a sample of cars
from the assembly line and noting for each car whether there are no defects, at least one major defect, or
only minor defects.
II. As students study more and more during their AP Statistics class, their chances of getting an A on
any given test continue to improve. The teacher is interested in the probability of any given student
receiving various numbers of A's on the class exams.
III. A committee of two is to be selected from among the five teachers and ten students attending a
meeting. What are the probabilities that the committee will consist of two teachers, of two' students, or
of exactly one teacher and one student?
(A) I only
(B) II only
(C) III only
(D) II and III
(E) None of the above gives the complete set of true responses.
21. Suppose X and Y are random variables with E(X) = 25, var (X) = 3, E(Y) = 30, and var (Y) = 4.
What are the expected value and variance of the random variable X + Y?
(A) E(X + Y) = 55, var (X + Y) = 3.5
(B) E(X +Y) = 55, var (X +Y) = 5
(C) E(X +Y) = 55, var (X +Y) = 7
(D) E(X +Y) = 27.5,var (X +Y) = 7
(E) There is insufficient information to answer this question.
22. Suppose X and Y are random variables with E(X) = 10, std.dev(X) = 3, E(Y) = 15, and std.dev(Y) =
4. Given that X and Y are independent, what are the mean and standard deviation of the random variable
X + Y?
(A) E(X+Y) = 25, std.dev(X+Y) = 3.5
(B) E(X+Y) = 25, std.dev(X+Y) = 5
(C) E(X+Y) = 25, std.dev(X+Y) = 7
(D)) E(X+Y) = 12.5 std.dev(X+Y) = 7
(E) There is insufficient information to answer this question.
23. Suppose X and Y are random variables with E(X) = 500, var (X) = 50, E(Y) = 400, and var (Y) = 30.
Given that X and Y are independent, what are the expected value and variance of the random variable X
- Y?
(A) E(X - Y) = 100, var (X - Y) = 20
(B) E(X - Y) = 100, var (X - Y) = 80
(C) E(X - Y) = 900, var (X - Y) = 20
(D) E(X - Y) = 900, var (X - Y) = 80
(E) There is insufficient information to answer this question.
24. Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while
the average for policewomen is 66 inches with a standard deviation of 3 inches. If a committee looks at
all ways of pairing up one male with one female officer, what will be the mean and standard deviation
for the difference in heights for the set of possible partners?
(A) Mean of 5 inches with a standard deviation of 1 inch
(B) Mean of 5 inches with a standard deviation of 3.5 inches (C) Mean of 5 inches with a standard
deviation of 5 inches (D) Mean of 68.5 inches with a standard deviation of 1 inch (E) Mean of 68.5
inches with a standard deviation of 3.5 inches
25. Suppose X and Y are random variables with E(X) = 720, std.dev(X)=6, E(Y)=240, and
std.dev.(Y)=8. Given that X and Y are independent, what are the mean and standard deviation of the
random variable X+Y?
(A) E(X+Y) = 960, std.dev(X+Y) = 7
(B) E(X+Y) = 960, std.dev(X+Y) = 10
(C) E(X+Y) = 960, std.dev(X+Y) = 14
(D)) E(X+Y) = 480, std.dev(X+Y) = 14
(E) There is insufficient information to answer this question.
26. Suppose a family eats frequently at a nearby fast food restaurant. There are three possible toys (a car,
a top, of a yo-yo) given with the kids’ meals. The toys are placed in the meal bags at random. Suppose
this family buys a kids’ meal at this restaurant on four different days.
(A) What is the probability that 3 out of 4 meals will come with a yo-yo?
(B) What is the probability that at most 2 meals will come with a yo-yo?
(C) What is the probability of getting at least 3 yo-yos with 4 meals purchased?
(D) What is the expected number of yo-yos when 4 meals are purchased?
(E) Compute the standard deviation of the number of yo-yos when 4 meals are purchased.
Answer Key
1b, 2a, 3d, 4a, 5e, 6b, 7d, 8a, 9d, 10c, 11e, 12c, 13e, 14b, 15c, 16a, 17d, 18c, 19e, 20e, 21e, 22b, 23b,
24c, 25b
26 a: .0988
26 b: 0889
26 c: .1111
26 d: 1.3333
26 e: .9428