# What is the z-score of sample X, if n = 144, mu= 71, St. Dev. =12, and E[X] =77?

Dec 1, 2016

The z-score is $= 6$

#### Explanation:

The z-score of a sample mean is

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

$\overline{x} = E \left[X\right] = 77$

$\mu = 71$

$\sigma = 12$

$n = 144$

Therefore,

$z = \frac{77 - 71}{\frac{12}{\sqrt{144}}} = \frac{6}{\frac{12}{12}} = 6$