IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. The middle 30% of IQs fall between what two values?

Answer 1

You want Z scores that cut off .15 (15%) of the students either direction from the mean.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and put its Z score with the other values in the above equation. Solve for the score (both ±).