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. Let X equal the number of customers who choose an oversize racket, so X ~ Bin( 10, 0, 60). Assume a binomial distribution. Among ten randomly selected customers who want this type of racket, what is the probability that at least six want the oversize version? b) The store currently has seven racket 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 the current stock?

Explanation / Answer

a) n = 10 , p = 0.6 ,

x = number (out of 10) who wants an oversize version

We want to find P ( X>=6) = ?

P ( X = k) = 10Ck 0.6k 0.410-k  ,

Here we have k = 6,7,8,9,10 since x>=6

So P ( X>=6) = 10C6 0.66 0.410-6 + 10C7 0.67 0.410-7 + 10C8 0.68 0.410-8 +10C9 0.69 0.410-9 +10C10 0.610 0.410-10

P (x>=6) = 0.2508 +0.215 +0.1209 + 0.0403 + 0.006

=0.633

b)

We have to find

P(3 <= x <= 7) = P(x<=7) - P (x<=2)

= 0.833-0.012

= 0.821

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