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

Answer:

99.7%

Step-by-step 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:

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

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

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.