# 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?

Jan 25, 2018

$0.0062$

#### Explanation:

given

X~N(100,10^2)

with sample size $25$

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

$P \left(\overline{X} < 95\right) = P \left(Z < \frac{95 - 100}{\frac{10}{5}}\right)$

$P \left(Z < - \frac{5}{2}\right) = P \left(Z < - 2.5\right)$

$= 1 - P \left(Z < 2.5\right)$

$1 - 0.9938$

$= 0.0062$