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MATH 2565 (19)


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York University
Mathematics and Statistics
MATH 2565
Jagmohan Chawla

PPS 7 Problem 17.27: A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves six times, what is the probability that she gets a) all six serves in? b) exactly four serves in? c) at least four serves in? d) no more than four serves in? Problem 17.29: Suppose the tennis player in Exercise 27 serves 80 times in a match. a) What are the mean and standard deviation of the number of good first serves expected? b) Verify that you can use a Normal model to approximate the distribution of the number of good first serves. c) Use the 68-95-99.7 Rule to describe this distribution. d) What is the probability that she makes at least 65 first serves? Problem 17.31: An orchard owner knows that he will have to use about 6% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 300 apples. a) Describe an appropriate model for the number of cider apples that may come from that tree. Justify your model. b) Find the probability there will be no more than a dozen cider apples. c) Is it likely there will be more than 50 cider apples? Explain. Problem 17.34: An airline, believing that 5% of passengers fail to show up for flights, overbooks (sell more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What is the probability that the airline will not have enough seats, so someone gets bumped? Problem 18.43: Statistics Canada reported the following distribution for family size in Canada. Size Percent
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