Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.08degreesF and a standard deviation of 0.61degreesF. 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 96.25degreesF and 99.91degrees​F? b. What is the approximate percentage of healthy adults with body temperatures between 96.86degreesF and 99.30degrees​F? a. Approximately nothing​% of healthy adults in this group have body temperatures within 3 standard deviations of the​ mean, or between 96.25degreesF and 99.91degreesF.

Answer 1

Solution :

Given that,

mean = = 98.08

standard deviation = = 0.61

Using Empirical rule,

a) P( - 3 < x <   + 3 ) = 99.7%

= P( 98.08 - 3 * 0.61 < x < 98.08 + 3 * 0.61 ) = 99.7%

= P( 98.08 - 1.83 < x < 98.08 + 1.83 ) = 99.7%

=P( 96.25 < x < 99.91 ) = 99.7%

Approximately = 99.7%

b) P( - 2 < x <   + 2 ) = 95%

= P( 98.08 - 2 * 0.61 < x < 98.08 + 2 * 0.61 ) = 95%

= P( 98.08 - 1.22 < x < 98.08 + 1.22 ) = 95%

=P( 96.86 < x < 99.30 ) = 95%

Approximately = 95%