Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.2998.29degrees°F and a standard deviation of 0.650.65degrees°F. Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 22 standard deviationsdeviations of the​ mean, or between 96.9996.99degrees°F and 99.5999.59degrees°​F? b. What is the approximate percentage of healthy adults with body temperatures between 96.3496.34degrees°F and 100.24100.24degrees°​F?

Answer 1

Solution :

Given that ,

mean = = 98.29

standard deviation = = 0.65

Using Empirical rule,

a) P( - 2 < x <   + 2 ) = 95%

= P( 98.29 - 2 * 0.65 < x < 98.29 + 2 * 0.65 ) = 95%

= P( 98.29 - 1.30 < x < 98.29 + 1.30 ) = 95%

=P( 96.99 < x < 99.59 ) = 95%

c) P( - 3 < x <   + 3 ) = 99.7%

= P( 98.29 - 3 * 0.65 < x < 98.29 + 3 * 0.65 ) = 99.7%

= P( 98.29 - 1.95 < x < 98.29 + 1.95 ) = 99.7%

=P( 96.34 < x < 100.24 ) = 99.7%