Question

for males in a certain town, the systolic blood pressure is normally distributed with a mean of 135 and a standard deviation of 8. using the empirical rule, what percentage of males in the town have a systolic blood pressure between 119 and 151?

Explanation:

Step1: Identify how many standard deviations away from the mean the values are.

First, calculate the number of standard deviations for 119:
\( \frac{119 - 135}{8} = \frac{-16}{8} = -2 \)
Then, calculate for 151:
\( \frac{151 - 135}{8} = \frac{16}{8} = 2 \)

Step2: Apply the empirical rule.

The empirical rule states that for a normal distribution, approximately 95% of the data lies within \( \mu \pm 2\sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation. Here, the values 119 and 151 are \( \mu - 2\sigma \) and \( \mu + 2\sigma \) respectively.

Answer:

95%