# What is the z-score of sample X, if n = 67, mu= 38, St. Dev. =18, and mu_X =76?

Nov 15, 2016

The z-score is $= 17.3$

#### Explanation:

The z-score for a sample mean is given by the formula

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\overline{x} = 76$

$\mu = 38$

$\sigma = 18$

$n = 67$

Therefore, the z-score $= \frac{76 - 38}{\frac{18}{\sqrt{67}}}$

$= \frac{38}{2.2} = 17.3$