Question

for males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 9. using the empirical rule, what percentage of males in the town have a systolic blood pressure between 78 and 132?

Explanation:

Step1: Find how many standard deviations 78 and 132 are from the mean.

The mean ($\mu$) is 105 and the standard deviation ($\sigma$) is 9.
For 78: $105 - 78 = 27$, and $\frac{27}{9}=3$. So 78 is 3 standard deviations below the mean.
For 132: $132 - 105 = 27$, and $\frac{27}{9}=3$. So 132 is 3 standard deviations above the mean.

Step2: Apply the empirical rule.

The empirical rule states that for a normal distribution:

• Approximately 68% of data lies within $\mu \pm \sigma$.
• Approximately 95% of data lies within $\mu \pm 2\sigma$.
• Approximately 99.7% of data lies within $\mu \pm 3\sigma$.

Since 78 and 132 are 3 standard deviations from the mean (i.e., within $\mu \pm 3\sigma$), the percentage of males with systolic blood pressure between 78 and 132 is approximately 99.7%.

Answer:

99.7%