A) Her Solution Is Mathematically Correct but Not Explained Very Well
Name: ______
AP Statistics
1) In the November 27, 1994, issue of Parade magazine, the “Ask Marilyn” section contained this question: “Suppose a person was having two surgeries performed at the same time. If chances of success for surgery A are 85%, and the chances of success for surgery B are 90%, what are the chances that both would fail?” What do you think of Marilyn’s solution: (.15)(.10) = .015?
A) Her solution is mathematically correct but not explained very well.
B) Her solution is both mathematically correct and intuitively obvious.
C) Her use of complementary events is incorrect.
D) Her use of the general addition formula is incorrect.
E) She assumed independence of events, which is most likely wrong.
2) A television game show has three payoffs with the following probabilities:
Payoff ($)0100010,000
Probability.6.3.1
What are the mean and standard deviation for the payoff variable?
A)µx = 1300, σx = 2934
B) µx = 1300, σx = 8802
C)µx = 3667, σx = 4497
D) µx = 3667, σx = 5508
E) None of the above gives a set of correct answers.
3) 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) $260B) $352
C) $500D) $540
E) $699
4) If the probability of a basketball player scoring on any shot is .75, what is the probability that she will score on at most 5 of her next 6 shots?
A) .3560B) .8220
C) .1780D) .4661
E) .5339
AP Review Questions
Random Variables & Binomial Distributions
5) 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) $23,800B) $27,110
C) $28,000D) $32,200
E) $56,000
6) 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 the policy?
A) $200B) $250
C) $300D) $350
E) $450
7) Find the probability that a family of five children will have exactly three boys.
A) .3125B) .6875
C) .8125D) .1875
E) .1563
8) 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 IIB) I and III
C) II and IIID) I, II, and III
E) None of the above gives the complete sets of true responses.
9) 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
10) Consider the following table of ages of U.S. senators:
Age (yr):<4040-4950-5960-6970-79>79
Number of senators530362252
What is the probability that a senator is under 70 years old given that he is at least 50 years old?
A) .580B) .624
C) .643D) .892
E) .969
11) 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 $1000. Assuming you will go bankrupt it you don’t show a profit, which option should you choose for the best chance of avoiding bankruptcy?
A) First choiceB) Second choice
C) Third choiceD) Either the first or second choice
E) All the choices give an equal chance of avoiding bankruptcy
12) Can the function 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
13) 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 the $0.37 postage it cost you to send in your name?
A) Yes, because , which is less than 7,500,000
B) No, because you’re expected winnings are only $0.14
C) Yes, because
D) No, because 1,052,000 < 7,500,000
E) Yes because
14) 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.
15) Which of the following is a discrete random variable?
A) the number of times a student guesses the answers to questions on a
certain test
B) the amount of gasoline purchased by a customer
C) the amount of mercury found in fish caught in the Gulf of Mexico
D) the height of water-oak trees
E) the time elapsed until the first field goal at home football games
16) A medicine is known to produce side effects in 1 in 5 patients taking it. Suppose a doctor prescribes the medicine to 4 unrelated patients. What is the probability that none of the patients will develop side effects?
A) 0.8B) 0.4096
C) 0.25D) 0.2
E) 0.0016