# What is the z-score of sample X, if n = 54, mu= 37, St. Dev. =30, and mu_X =42?

Nov 10, 2015

$z = 1.225$

#### Explanation:

${\mu}_{x}$ represents one of the value of the distribution.
${\mu}_{\overline{x}} = \mu$
We have to find the Standard Error of the given distribution.

It is - SD$= \frac{\sigma}{\sqrt{n}} = \frac{30}{\sqrt{54}} = \frac{30}{7.35} = 4.08$

$z = \frac{{\mu}_{x} - \mu}{\sigma} = \frac{42 - 37}{4.08} = 1.225$