# What is the z-score of sample X, if n = 64, mu= 56, SD =20, and E[X] =320?

Nov 13, 2015

I believe the $\sum \left(x\right) = 320$ is wrongly given.

#### Explanation:

There are 64 observations. The Total of the 64 observations cannot be $\sum \left(x\right) = 320$

Any the steps involved are -

$\sum \left(x\right) = 320$
$\overline{x} = \frac{\sum \left(x\right)}{n} = \frac{320}{64} = 5$

$S E = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{64}} = \frac{20}{8} = 2.5$

$z = \frac{\overline{x} - \mu}{S E} = \frac{5 - 56}{2.5} = - 20.4$

This answer may be wrong because of wrong information.