IQ scores and distribution

Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 103 and a standard deviation of 14 . Using the empirical rule, what percentage of IQ scores are between 61 and 145?

Answer 1

The distance between 61 and 103 is 42. Since the SD is 14, 61 is 42/14 = 3 SD below the mean.

The distance between 145 and 103 is also 42, making is 3 SD below the mean.

Per the empirical rule, 99.7% of the data is between +/- 3 SD of the mean.