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Unformatted text preview: MATH 33551 FINAL EXAM Spring 2009 You may leave answers in terms of binomial coefficients, when applicable. ** SHOW ALL WORK ** (17) 1. A 2007 study showed that 17% of the citizens of Hawaii are smokers. Let X be the number of smokers in a randomly selected group of 35 Hawaii citizens. (i) Treating X as a binomial random variable, find the probability that X is at least 2. (ii) Now treat X as a Poisson random variable and again compute the probability that X is at least 2. (iii) People are picked at random from this group of 35 citizens until a smoker is found. What is the probability that the first smoker found is the 4th person picked? (iv) Approximating the binomial random variable X by a normal random variable, find the probability that X = 7. (Recall that the standard deviation of a binomial r.v. is npq . A table for the function appears on the last page of this exam.) (9) 2. Let A and B be events in a sample space such that P ( A ) = 0 . 4 , P ( B ) = 0 . 7, and P ( AB ) = 0...
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