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 25 people is selected, find the probability that the mean time taken by him/her is less than 14 minutes?

Answer 1

Solution :

Given that ,

mean =   = 12.5

standard deviation = = 3.5

n = 25

= 12.5

=  / n = 3.5 / 25=0.7

P( <14 ) = P[( - ) / < (14-12.5) /0.7 ]

= P(z < 2.14)

Using z table  

=0.9838   

probability= 0.9838