Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.25degreesF and a standard deviation of 0.48degreesF. Using the empirical​ rule, find each approximate percentage below.

a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the​ mean, or between 96.81degreesF and 99.69degrees​F?

b. What is the approximate percentage of healthy adults with body temperatures between 97.29degreesF and 99.21degrees​F?

Answer 1

Solution :

Given that,

mean = = 98.25

standard deviation = = 0.48

Using Empirical rule,

a) P( - 3 < x <   + 3 ) = 99.7%

= P( 98.25 - 3 * 0.48 < x < 98.25 + 3 * 0.48 ) = 99.7%

=P( 96.81 < x < 99.69) = 99.7%

Approximately = 99.7%

b) P( - 2 < x <   + 2 ) = 95%

= P( 98.25 - 2 * 0.48 < x < 98.25 + 2 * 0.48 ) = 95%

=P( 97.29 < x < 99.21 ) = 95%

Approximately = 95%