Question

1. for males in a certain town, the systolic blood pressure is normally distributed with a mean of 110 and a standard deviation of 9. using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7% of males.

options:
○ (101, 119)
○ (92, 128)
○ (83, 137)
○ (74, 146)
clear all

Explanation:

Step1: Recall Empirical Rule for 99.7%

The empirical rule states that for a normal distribution, about 99.7% of the data lies within \( \mu \pm 3\sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.
Given \( \mu = 110 \) and \( \sigma = 9 \).

Step2: Calculate Lower Bound

Lower bound \( = \mu - 3\sigma = 110 - 3\times9 = 110 - 27 = 83 \).

Step3: Calculate Upper Bound

Upper bound \( = \mu + 3\sigma = 110 + 3\times9 = 110 + 27 = 137 \).

Answer:

(83, 137)