Question

question
for males in a certain town, the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 5. using the empirical rule, determine the interval of systolic blood pressures that represent the middle 68% of males.

Explanation:

Step1: Recall empirical rule for 68%

For normal distributions, 68% of data lies within $\mu \pm \sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Identify given values

$\mu = 120$, $\sigma = 5$

Step3: Calculate lower bound

Subtract $\sigma$ from $\mu$:
$120 - 5 = 115$

Step4: Calculate upper bound

Add $\sigma$ to $\mu$:
$120 + 5 = 125$

Answer:

The interval of systolic blood pressures is (115, 125)