soln%208 - X X X X X X X X X X X X X X X X X AP Statistics...

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X X X X X X X X X X X X X X X X X AP Statistics Solutions to Packet 8 X The Binomial and Geometric Distributions The Binomial Distributions The Geometric Distributions X X X X X X X X X X X 54p X X
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2 HW #1 1 – 5, 7, 8 8.1 BINOMIAL SETTING? In each situation below, is it reasonable to use a binomial distribution for the random variable X ? Give reasons for your answer in each case. (a) An auto manufacturer chooses one car from each hour’s production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc.) in the car’s paint. No: There is no fixed n (i.e., there is no definite upper limit on the number of defects). (b) The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty; X is the number who say “Yes.” Yes B: Only two choices, yes or no I: It is reasonable to believe that all responses are independent (ignoring any “peer pressure”) N: n = 100 S: All have the same probability of saying “yes” since they are randomly chosen from the population (c) Joe buys a ticket in his state’s “Pick 3” lottery game every week; X is the number of times in a year that he wins a prize. Yes B: Only two choices, win or lose I: All responses are independent N: n = 52 S: In a “Pick 3” game, Joe’s chance of winning the lottery is the same every week 8.2 BINOMIAL SETTING? In each of the following cases, decided whether or not a binomial distribution is an appropriate model, and give your reasons. (a) Fifty students are taught about binomial distributions by a television program. After completing their study, all students take the same examination. The number of students who pass is counted. YES B: Only two choices, pass or fail I: It is reasonable to assume that the results for the 50 students are independent N: n = 50 S: Each student has the same chance of passing (b) A student studies binomial distributions using computer-assisted instruction. After the initial instruction is completed, the computer presents 10 problems. The student solves each problem and enters the answer; the computer gives additional instruction between problems if the student’s answer is wrong. The number of problems that the students solves correctly is counted. No: Since the student receives instruction after incorrect answers, her probability of success is likely to increase. (c) A chemist repeats a solubility test 10 times on the same substance. Each test is conducted at a temperature 10º higher than the previous test. She counts the number of times that the substance dissolves completely. No: Temperature may affect the outcome of the test.
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3 8.3 INHERITING BLOOD TYPE Each child born to a particular set of parents has probability 0.25 of having blood type O. Suppose these parents have 5 children. Let X = number of children who have type O blood. Then X is B (5, 0.25).
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soln%208 - X X X X X X X X X X X X X X X X X AP Statistics...

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