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?

1 Answer
Jun 10, 2017

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.