A particular type of tennis racket comes in a midsize version and an oversize ve

Question

A particular type of tennis racket comes in a midsize version and an oversize version. Seventy percent of all customers who order this racket from a certain store purchase the oversize version, and 30% puxchase the midsize version. (a) Among twelve randomly selected customers who want this type of racket, what is the probability that at least ten want the oversize version? (b) Suppose midsize rackets sell fot $109 and oversize rackets sell for $129, and the store currently has 20 of each in stock. What is the expected revenue from the next 12 customers who purchase this racket? What is the standard deviation of revenue from the next 12 customers who purchase this racket? Suppose you begin observing orders of this racket at some point in time. Answer questions (c) - (f). (c) If the third oversize racket ordered is the fifth racket ordered, what is the probability that exactly 11 of the fust 16 rackets ordered are oversize? (d) What is the probability that the second oversize racket occurs after the fourth order? (e) If 6 of the first 8 orders are for oversize rackets, on average, how many of the first 100 rackets will be for oversize rackets? (f) If 6 of the first 8 orders are for oversize rackets, what is the probability that the 8th oversize racket ordered is the 12^th racket ordered overall.

Explanation / Answer

X- no of persons who purchase oversize version is binomial with (12, 0.7)

P(X=r ) = nCr p^r q^(n-r)

a) P(X>=10) = 0.2528

b) E(X) = np = 8.4

Y - mid size numbers

E(Y) = np' = 12(0.3) = 3.6

Expected revenue = 8.4(129)+3.6(109)

= 1476

E(Revenue^2) =182556

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