Question

The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.09∘F and a standard deviation of 0.64∘F. 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 96.17∘F and 100.01∘F ?

Answer 1

The approximate percentage of healthy adults with body temperatures between 96.17°F and 100.01°F is 99.7% (within three standard deviations of the mean).

Step-by-step explanation:

The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. In this case, the mean body temperature is 98.09°F and the standard deviation is 0.64°F.

So, to find the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, we calculate:

lower bound: mean - (3 x standard deviation) = 98.09 - (3 x 0.64) = 96.17°F

upper bound: mean + (3 x standard deviation) = 98.09 + (3 x 0.64) = 100.01°F

Therefore, the approximate percentage of healthy adults with body temperatures between 96.17°F and 100.01°F is 99.7% (within three standard deviations of the mean).