Question

for males in a certain town, the systolic blood pressure is normally distributed with a mean of 125 and a standard deviation of 7. using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7% of males.

answer attempt 1 out of 2

Explanation:

Step1: Recall the empirical rule for 99.7%

The empirical rule states that for a normal distribution, approximately 99.7% of the data lies within 3 standard deviations of the mean. The formula for the interval is $\mu - 3\sigma$ to $\mu + 3\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Identify $\mu$ and $\sigma$

Given $\mu = 125$ and $\sigma = 7$.

Step3: Calculate the lower bound

Lower bound = $\mu - 3\sigma = 125 - 3\times7 = 125 - 21 = 104$.

Step4: Calculate the upper bound

Upper bound = $\mu + 3\sigma = 125 + 3\times7 = 125 + 21 = 146$.

Answer:

The interval is from 104 to 146.