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PractioeProblems_Exam > s/blackboard/execute/content/file?cmd-view&content.id-;_5828449 1&course; id_157947.1 UAConnectl Univers-BlackboardLearn Credit Sesame-Ove app University of Arkans D volkswagen Credit- MITO marble is selected? Problem 2. 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 th oversize version, and 30% purchase the midsize version. Among twelve randomly selected customers who want this type of racket, what is the probability that at least ten want the oversize version? (a) (b) Suppose midsize rackets sell for $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)- What is the probability that the second oversize racket occurs after the fourth order? (Can you figure out how to do this with both binomial and negative binomial? Which is easier?) (c) What is the probability that the third oversize racket occurs after the ninth order? (Can you figure out how to do this with both binomial and negative binomial? Which is easier?) (d) (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?

Explanation / Answer

Solution

P(Oversize) = 0.7 and P(midsize) = 0.3

(a) n = 12 Let X number of people want the oversize

P(X>=10) = P(X=10)+P(X=11)+P(x=12)

= 12C10(0.7)10(0.3)2 + 12C11(0.7)11(0.3) + 12C12(0.7)12 = 0.2528

(b) E(revenue) = (109*0.3+129*0.7)*20 = 2460

variance = E(R2)-(E(R))2

= 400(1092(0.3)+1292(0.7)) - 24602 = 33600

Standard deviation = 183.30

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