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. Sixty percent of all customers at a certain store want the oversize version. (Round your answers to three decimal places.) (a) Among nine randomly selected customers who want this type of racket, what is the probability that at least six want the oversize version? (b) Among ten randomly selected customers, what is the probability that the number who want the oversize version is within 1 standard deviation of the mean value? (c) The store currently has eight rackets of each version. What is the probability that all of the next ten customers who want this racket can get the version they want from current stock?

Explanation / Answer

Pr(People want an oversize version) = 0.60

(a) Here n = 9 if X is the number of people who want a oversize version

So the given distribution is binomial.

Pr(X >=6) = 1 - BIN(x < 6; 9 ; 0.6) = 1 - 0.5174 = 0.4826

(B) N = 10 here , Here standard deviation of mean value = sqrt (10 * 0.6 * 0.4) = 1.55

here one standard deviation away values are = 6 +- 1.55 = (4.45, 7.55)

so possible values are 5,6 & 7

Pr(X = 5, 6, 7) = BIN(X = 5; 10; 0.6) + BIN(X = 6; 10 ; 0.6) + BIN(X = 7; 10 ; 0.6) = 0.2007 +0.2508 + 0.2150 = 0.6665

(c) Here we have eight rackets of each version. NOw there are 10 customers who want to buy rackets. No we have tot find the probability that customers get what they want so that means oversize vesion shall be less than equal to 8 , similarly undersize racket must be less than 8 also.

Pr(Probability all customers get what they want) = BIN(2 <= X <= 8; 10; 0.6)  

= 0.9520

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