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 ten 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?

Answer 1

Let X is a random variable shows the number of rackets of oversize version out of 10. Here X has binomial distribution with following parameters:

n=10 and p=0.60

(a)

The probability that at least six want the oversize version is

Answer: 0.633

(b)

The mean is

The standard deviation is

The interval corresponding to one standard deviation of mean is

The required probability is

Answer: 0.666

(c)

The all customers who want this racket can get the version they want from current stock if customer who want oversize racket is between 2 and 8 inclusive. So, the probability that all of the next ten customers who want this racket can get the version they want from current stock is

Answer: 0.952