What is the z-score of sample X, if n = 196, mu= 45, St. Dev. =28, and E[X] =29?

Dec 29, 2016

The answer is $= - 8$

Explanation:

The z-score for a sample mean is

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

$\overline{x} = E \left[X\right] = 29$

$\mu = 45$

$\sigma = 28$

$n = 196$

Therefore,

$z = \frac{29 - 45}{\frac{28}{\sqrt{196}}}$

$= - \frac{16}{\frac{28}{14}}$

$= - \frac{16}{2} = - 8$