Question

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?

Answer 1

78.81%

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=(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`.