Help with statistics please

Question

Assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find P40, which is the iq score seperating the bottom 40% from the top 60%. Round to the nearest tenth.

Answer 1

That IQ score would be the 40th percentile.

let x = that IQ score

use the formula z = (x - mean)/SD, where mean = 15 and SD = 15.

the z-score corresponding to the 40th percentile (cumulative probability of 0.4) is -0.25

so -0.25 = (x - 100)/15

-0.25(15) + 100 = x

= 96.25

~ 96