# A set of test scores is normally distributed with a mean of 78 and a standard deviation of 4.5. Dwayne scored 87 on the test. What is his percentile score?

Jun 11, 2017

$.9772$ or about 97.72%

#### 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:

$z = \frac{87 - 78}{4.5}$

$z = 2$

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 $.9772$
All you have to do now is multiply by $100$.