the scores for a normal distribution question

Question

 The scores for a normal distribution of a population of IQ scores and there was a mean of 105 and a standard deviation of 12.

      Identify the percentage of people that would have an IQ score greater than 120 and less than 90.

Answer 1

Observe that 105 + 15 = 120 and 105 - 15 = 90, and that 15/12 = 1.25

That means we can rewrite the problem as: identify the percentage of people with IQ score more than 1.25 std deviations from the mean.

P{ IQ score > mean + 1.25*std dev } = .1056 (table lookup of right-hand tail probability, or plug into statistical software).

We want P{ (IQ score > mean + 1.25*std dev) or (IQ score < mean - 1.25*std dev) } = .2112

(I multiplied the right-hand tail probability by 2; this is legitimate because the normal distribution is symmetric about the mean)