Question

For males in a certain town, the systolic blood pressure is normally distributed with a

mean of 110 and a standard deviation of 5. Using the empirical rule, determine the
interval of systolic blood pressures that represent the middle 99.7% of males.

Answer 1

The empirical rule states that for a normal distribution with mean μ and standard deviation σ, about 68% of the data lies within one standard deviation of the mean (i.e., within the interval [μ - σ, μ + σ]), about 95% of the data lies within two standard deviations of the mean (i.e., within the interval [μ - 2σ, μ + 2σ]), and about 99.7% of the data lies within three standard deviations of the mean (i.e., within the interval [μ - 3σ, μ + 3σ]).

In this case, the mean of the distribution is 110 and the standard deviation is 5, so the interval of systolic blood pressures that represent the middle 99.7% of males is:

[110 - 3(5), 110 + 3(5)]
= [95, 125]

Therefore, the interval of systolic blood pressures that represent the middle 99.7% of males is [95, 125].