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.

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

To solve the problem we will find intervals for each percentage of data according to the Empirical rule.

The interval of systolic blood pressures of 99.7% of the male is between 112 and 148.

Given to us

the systolic blood pressure is normally distributed with a mean of 130,the systolic blood pressure is normally distributed with a standard deviation of 6

To find

The interval of systolic blood pressures represents the middle 99.7 of males.

According to the Empirical rule,First Range

68% of the data will fall in the first interval,

To calculate the first interval lower range subtract the standard deviation from the mean, while for the upper range add them.

130 - 6 = 124

130 + 6 = 136

Second Range

95% of the data will fall in the second interval,

To calculate the second interval lower range subtract two times the standard deviation from the mean, while for the upper range add them.

130 - 2(6) = 112

130 + 2(6) = 148

Third Range

95% of the data will fall in the third interval,

To calculate the third interval lower range subtract three times the standard deviation from the mean, while for the upper range add them.

130 - 3(6) = 118

130 + 3(6) = 142

Hence,  the interval of systolic blood pressures of 99.7% of the male is between 112 and 148.

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