Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 103 103 and a standard deviation of 14 14 . Using the empirical rule, what percentage of IQ scores are less than 145 145 ? Please do not round your answer.

Answer 1

145 is 3 standard deviations above 103, since the difference, 42, is 3 times 14.

The rule I suppose is 68-95-99.7 the last number meaning 99.7% of the area of the Gaussian is between -3 and +3 standard deviations.

That's 0.3% leftover, 0.15% in each tail so

Answer: 99.85%

of the scores are (expected to be) less than 145.