The body temperatures of a group of healthy adults have a bell-shaped distributi

Question

The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.09 degrees°F and a standard deviation of 0.49 degrees°F. 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 97.11 degrees°F and 99.07 degrees°F?

b. What is the approximate percentage of healthy adults with body temperatures between 97.60 degrees°F and 98.58 degrees°F?

a. Approximately ? % of healthy adults in this group have body temperatures within 2 standard deviations of the mean, or between 97.11degrees°F and 99.07degrees°F.

(Type an integer or a decimal. Do not round.)

b. Approximately ? of healthy adults in this group have body temperatures between 97.60degrees°F and 98.58 degrees°F.

(Type an integer or a decimal. Do not round.)

Explanation / Answer

a) According to the empirical rule 68-95-99.7, 95% of the observations lies within 2 standard deviations of the mean. Therefore 95% is the required percentage here.

b) 97.6 = 98.09 - 0.49 that is 1 standard deviation less than the mean while 98.58 = 98.09 + 0.49 which means 1 standard deviation greater than the mean. By empirical rule approximately 68% of the observations lies within 1 standard deviation of the mean. Therefore 68% is the required percentage here.

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