Question

the body temperatures of a group of healthy adults have a bell - shaped distribution with a mean of 98.07°f and a standard deviation of 0.53°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 96.48°f and 99.66°f?
b. what is the approximate percentage of healthy adults with body temperatures between 97.01°f and 99.13°f?
a. approximately % of healthy adults in this group have body temperatures within 3 standard deviations of the mean, or between 96.48°f and 99.66°f.
(type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the empirical rule

The empirical rule for a normal distribution (bell - shaped distribution) states that approximately \(99.7\%\) of the data lies within \(3\) standard deviations of the mean.

Step2: Calculate the range for part (a)

The mean \(\mu = 98.07^{\circ}F\) and the standard deviation \(\sigma=0.53^{\circ}F\).
The lower bound is \(\mu - 3\sigma=98.07-3\times0.53 = 98.07 - 1.59=96.48^{\circ}F\)
The upper bound is \(\mu + 3\sigma=98.07 + 3\times0.53=98.07+1.59 = 99.66^{\circ}F\)

Answer:

\(99.7\)