# What is the z-score of sample X, if n = 121, mu= 55, St. Dev. =110, and E[X] =107?

Nov 24, 2016

The z-score is $= 5.2$

#### Explanation:

The z-score for a sample mean is given by

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

where

$\overline{x} = \left[X\right] = 107$

$\mu = 55$

$\sigma = 110$

$n = 121$

$z = \frac{107 - 55}{\frac{110}{\sqrt{121}}} = \frac{52}{\frac{110}{11}} = \frac{52}{10} = 5.2$