Question

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?

Answer 1

`.9772` or about `97.72%`

Explanation:

The question requires z-scores.

The formula is:

`z=(x-mu)/sigma`

Where `x=`the given value
`mu=` the mean
`sigma=` the standard deviation

Or

`z=("your value " - " the actual mean")/(SD)`

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

Plug in the values:

`z=(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`.