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

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

The linear equation is: y=ax+b