PROBLEM 10.2 (pg 121, #54) A particular type of tennis racquet comes in a midsiz

Question

PROBLEM 10.2 (pg 121, #54) A particular type of tennis racquet comes in a midsize version and an oversize version. Seventy percent of all customers at a certain store want the oversize version. Consider the next 7 customers to buy this type of racquet. Let X the number of the next 7 to buy the oversize version of the racquet The random variable X has a binomial distribution with parameters n and p What is the chance that at least 6 (6 or more) want the oversize version or P(X 6)? The store currently has 5 oversize and 3 midsize racquets in stock. What is the chance that all of the next seven customers can get their desired version from the current stock? NOTE: we seek PC sXs ) which equals a. b. c.

Explanation / Answer

a) n = 7

p = 0.7

b) P(X > 6) = P(X = 6) + P(X = 7)

                   = 7C6 * 0.76 * 0.31 + 7C7 * 0.77 * 0.30

                   = 0.3294

c) P(4 < X < 5) = P(X = 4) + P(X = 5)

                         = 7C4 * 0.74 * 0.33 + 7C5 * 0.75 * 0.32

                         = 0.2269 + 0.3177

                         = 0.5446

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