Problem

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 110 and a standard deviation of 8 . Using the empirical rule, determine the interval of systolic blood pressures that represent the middle $95 \%$ of males.

Solution

Step 1 :Given that the mean systolic blood pressure for males in the town is \(110\) and the standard deviation is \(8\).

Step 2 :Using the empirical rule, we know that approximately \(95\%\) of the data falls within two standard deviations of the mean.

Step 3 :Calculate the lower bound of the interval by subtracting two standard deviations from the mean: \(110 - 2 \times 8 = 94\).

Step 4 :Calculate the upper bound of the interval by adding two standard deviations to the mean: \(110 + 2 \times 8 = 126\).

Step 5 :\(\boxed{\text{The interval of systolic blood pressures that represent the middle 95\% of males is (94, 126).}}\)

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Source: https://solvelyapp.com/problems/15556/

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