# What is the z-score of sample X, if n = 49, mu= 15, SD =35, and E[X] =38?

Dec 20, 2016

The answer is $= \frac{3}{5}$

#### Explanation:

The z-score for a sample mean is

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

$\overline{x} = E \left[X\right] = 38$

$\mu = 15$

$\sigma = 35$

$n = 49$

Therefore,

$z = \frac{38 - 35}{\frac{35}{\sqrt{49}}}$

$= \frac{3}{\frac{35}{7}}$

$= \frac{3}{5}$