# What is the z-score of sample X, if n = 49, mu= 35, SD =105, and E[X] =39?

Nov 29, 2016

The z-score is $= \frac{4}{15}$

#### Explanation:

The z-score for a sample mean is

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

$\overline{x} = E \left[X\right] = 39$

$\mu = 35$

$\sigma = 105$

$n = 49$

So,

$z = \frac{39 - 35}{\frac{105}{\sqrt{49}}}$

$= \frac{4}{\frac{105}{7}}$

$= \frac{4}{15}$