Question

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

mean of 120 and a standard deviation of 7. Using the empirical rule, what percentage of
males in the town have a systolic blood pressure between 99 and 141?

Answer 1

99.7%

Explanation:

According to the Empirical Rule:

• 68% of data in a normal distribution are ±1σ from the mean μ
• 95% of data in a normal distribution are ±2σ from the mean μ
• 99.7% of data in a normal distribution are ±3σ from the mean μ

By calculating the z-score of each observed value, we can determine how many standard deviations these observed values are from the mean:

`\displaystyle Z=\frac{\text{Observed Value}-\text{Mean of the Sample}}{\text{Standard Deviation of the Sample}}\\\\Z=(99-120)/(7)\\ \\Z=(-21)/(7)\\\\Z=-3`

`\displaystyle Z=\frac{\text{Observed Value}-\text{Mean of the Sample}}{\text{Standard Deviation of the Sample}}\\\\Z=(141-120)/(7)\\ \\Z=(21)/(7)\\\\Z=3`

Clearly, we can see that 99.7% of males in the town have a systolic blood pressure between 99 and 141 by the Empirical Rule.