Question

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 130 and a standard deviation of 6. using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7 of males.

Answer 1

Average systolic blood pressure = x = 130
Standard deviation = s = 6

We are to find interval that represents the systolic blood pressure of middle 99.7% of the males.

According to the empirical rule:
a) 68% values lie within 1 standard deviation of the mean
b) 95% values lie within 2 standard deviation of the mean
c) 99.7% values lie within 3 standard deviation of the mean

So, 99.7% value will lie within 3 standard deviations from the mean.

We can express this range as:
( x - 3s, x + 3s)
= (130 - 3(6), 130 +3(6))
= ( 130 - 18, 130 + 18)
= ( 112, 148 )

Thus the interval from 112 to 148 contains the systolic blood pressure of middle 99.7% of the males in the certain town