Question

scores on an aptitude test are normally distributed with a means of 400 and a standard deviation of 60. explain how you would find any given percentile

Answer 1

We are given that scores are normally distributed.

We are given

Mean = 400

SD = 60

The formula for finding any percentile X is given as below:

X = Mean + Z*SD

X = 400 + Z*60

So, you need to find the Z value for the given percentile by using z-table or excel; and then you can find required percentile by using above formula.

Suppose, you want to find the 75^th percentile; then corresponding z value by using z-table or excel is given as 0.67449.

So, required percentile is given as below:

X = 400 + Z*60

X = 400 + 0.67449*60

X = 440.4694

75^th percentile = 440.4694