Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.37degreesF and a standard deviation of 0.51degreesF. Using the empirical​ rule, find each approximate percentage below.

a. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the​ mean, or between 97.35degreesF and 99.39degrees​F?

b. What is the approximate percentage of healthy adults with body temperatures between 96.84degreesF and 99.90degrees​F? a. Approximately nothing​% of healthy adults in this group have body temperatures within 2 standard deviations of the​ mean, or between 97.35degreesF and 99.39degreesF. ​(Type an integer or a decimal. Do not​ round.)

b. Approximately nothing​% of healthy adults in this group have body temperatures between 96.84degreesF and 99.90degreesF. ​(Type an integer or a decimal. Do not​ round.)

Answer 1

a) According to the empirical rule about 95% of the data fall within 2 standard deviation from the mean.

So approximately

95% of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.35 degreesF and 99.39 degrees F .

b) 98.37 - 3 * 0.51 = 96.84

98.37 + 3 * 0.51 = 99.90

According to the empirical rule about 99.7% of the data fall within 3 standard deviation from the mean.

So approximately 99.7% of healthy adults in this group have body temperatures between 96.84 degrees F and 99.90 degrees F.