# A normal distribution has a mean of 140 and a standard deviation of 40. How do you calculate the percentile rank of a score of 172?

Jun 10, 2017

78.81%

#### Explanation:

The question requires z-scores.

The formula is:

$z = \frac{x - \mu}{\sigma}$

Where $x =$the given value
$\mu =$ the mean
$\sigma =$ the standard deviation

Or

$z = \frac{\text{your value " - " the actual mean}}{S D}$

This is a bit easier to remember :)
(SD=Standard Deviation)

Plug in the values:

$z = \frac{172 - 140}{40}$

$z = .8$

Now you look up the probability that corresponds to the $z$ score in the table. (Which you should be provided with.)
The probability that corresponds to the $z$ score is $.7881$
All you have to do now is multiply by $100$.