Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Using the empirical rule, what percentage of people have an IQ score between 70 and 130?​

Answer 1

70 = 100 - 2•15 is 2 s.d.'s below the mean.

130 = 100 + 2•15 is 2 s.d.'s above the mean.

By the empirical rule,

Pr [70 ≤ X ≤ 130] = Pr [-2 ≤ Z ≤ 2] ≈ 95%

(where Z is normally distributed with mean 0 and s.d. 1)