Question

Given a normal distribution with mean = 100 and standard deviation = 10, if you select a sample of n = 25, what is the probability that x-bar is less than 95?

Answer 1

`0.0062`

Explanation:

given

`X~N(100,10^2)`

with sample size `25`

`barX~N(100,10^2/25)`

`P(barX<95)=P(Z<(95-100)/(10/5))`

`P(Z<-5/2)=P(Z<-2.5)`

`=1-P(Z<2.5)`

`1-0.9938`

`=0.0062`