# What is the z-score of sample X, if n = 100, mu= 61, St. Dev. =43, and E[X] =98?

Nov 15, 2016

The z-score is $= 8.6$

#### Explanation:

The z-score for a sample mean is calculated by the formula

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

$\overline{x} = E \left(x\right) = 98$

$\mu = 61$

$\sigma = 43$

$n = 100$

Therefore, $z = \frac{98 - 61}{\frac{43}{\sqrt{100}}}$

$= \frac{37}{4.3} = 8.6$