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. (a) Among eleven randomly selected customers who want this type of racket, what is the probability that at least six want the oversize version? (Enter your answer to four decimal places.) (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? (Enter your answer to four decimal places.) (c) The store currently has seven 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? (Enter your answer to four decimal place

Explanation / Answer

n=11 (number of customers) p = .6 (probability that 'a' customer would want an oversize version x = number (out of 10) who wants an oversize version P( x >= 6) P( x=k) = 11Ck (.6)^k (.4)^(10-k) k=6,7,8,9,10,11 Add all the probabilities for each case and get , P( x>=6) b) Mean = np = 10(.6) = 6 Variance = np(1-p) =10(.6)(.4) = 2.4 Standard deviation = sqrt(2.4) = 1.5492 Within 1 standard deviation of the mean is (6-1.5492, 6+1.1592) = (4.84, 7.15) (5,8) P( 5

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