Question

The times that a person spends in the shower are normally distributed with a mean of 12.5 minutes and a standard deviation of 3.5 minutes. If 9 people is selected, find the probability that the mean time taken by him/her is greater than 15.2 minutes?

Answer 1

Solution :

The times that a person spends in the shower are normally distributed with a mean of 12.5 minutes and a standard deviation of 3.5 minutes.

Number of people ( n ) =9

To find : P [ > 15.2 ]

We do not know the probability distribution of Xi's. We use central limit theorem, thus we assume follows approximately N(0,1)

P ( > 15.2) =

=

=

=

= P ( Z > 2.314285 )

P ( > 15.2 ) = 1- P( Z < 2.31 )

= 1 - 0.9896......... by using z table

P ( > 15.2 ) = 0.0104

The probability that the mean time taken by him/ her is greater than 15.2 minutes is 0.0104