In a study of

500

men, diastolic blood pressure was found to be approximately normally distributed, with a mean of 82 millimeters (mm) of mercury and standard deviation of 10 millimeters.

Use the 68-95-99.7% rule to determine what percentage of the test group had a diastolic pressure between

52 millimeters

and

112 millimeters

of mercury.

We know that:

Mean = 82 mm and SD = 10 mm (standard deviation)

82 - 3 * SD = 82 - 3 * 10 = 82 - 30 = 52 mm

82 + 3 * SD = 82 + 3 * 10 = 82 + 30 = 112 mm

Population between 52 and 112 mm is within + / - 3 standard deviations from the mean.

By the 66 - 95 - 99.7 % rule it is: 99.7% of the test group.

0.977 * 500 = 498.5

Answer:

99.7 % of the test group have a diastolic pressure between 52 and 112 mm, or 498 men.