Question

Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65?

Answer 1

30.85%

Explanation:

Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10

mean = 70 and SD= 10

To find percentile we use z-score value

z value can be find using formula

`z= (x-mean)/(SD)`

`z= (65-70)/(10)`

z=-0.5

Now we use z- score table to find the value when z=-0.5

P(x=65) = 0.3085

To find percentile we multiply by 100

0.3085 * 100 = 30.85%