Question

In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches. Using the empirical rule, determine the interval of heights that represents the middle 99.7% of male heights from this school.

Answer 1

The empirical rule (68–95–99.7) says about 99.7% lie within ±3 standard deviations of the mean.
Mean ± 3σ = 69 ± 3(2.5) = 69 ± 7.5, so approximately 61.5 inches to 76.5 inches.