Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.1698.16degrees°F

and a standard deviation of

0.590.59degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a.	What is the approximate percentage of healthy adults with body temperatures within 33 standard deviationsdeviations of the​ mean, or between 96.3996.39degrees°F and 99.9399.93degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 97.5797.57degrees°F and 98.7598.75degrees°​F?

Answer 1

According to empirical rule, 68%, 95% and 99.7% of data lies within 1, 2 and 3 standard deviations of mean respectively.

a) Percentage of healthy adults with body temperatures within 3 standard deviations of the​ mean (between 96.39 °F and 99.93 °​F) = 99.7%

b) 98.16 - 1x0.59 = 97.57 °F

98.16 + 1x0.59 = 98.75 °F

97.57 °F to 98.75 °F is the interval one standard deviation from mean.

Percentage of healthy adults with body temperatures between 97.57 °F and 98.75 °F = 68%