Question

For males in a certain town, the systolic blood pressure is normally distributed with amean of 135 and a standard deviation of 9. Using the empirical rule, determine theinterval of systolic blood pressures that represent the middle 95% of males.

Answer 1

From the question, we are given the following parameters;

Mean x = 135

standard deviation s = 9

The following are true based on the empirical rule;

1) 68% values lie within 1 standard deviation of the mean

2) 95% values lie within 2 standard deviation of the mean

Since we are to determine the interval of systolic blood pressures that represent the middle 95% of males, we will apply the second empirical rule as shown;

The interval will be between (x-2s, x+2s)

Substitute the given parameters into the interval a shown;

Interval of values = (135-2(9), 135+2(9))

Interval of values = (135-18, 135+18)

Interval of values = (117, 153)

Hence the interval from 117 to 153 contains the systolic blood pressure of middle 95% of the males in the town