# What is the z-score of sample X, if n = 100, mu= 45, SD =30, and E[X] =31?

Dec 15, 2016

The z-score is $= - 5$

#### Explanation:

The z-score for a sample mean is

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

$\overline{x} = E \left[X\right] = 31$

$\mu = 45$

$\sigma = 30$

$n = 100$

$z = \frac{31 - 45}{\frac{30}{\sqrt{100}}} = \frac{- 15}{3} = - 5$