the body temperatures of a group of healthy adults have a bell - shaped distribution with a mean of 98.39°f…

Explanation:

Step1: Recall the empirical rule

The empirical rule for a normal - distribution states that approximately 68% of the data lies within 1 standard deviation of the mean, approximately 95% of the data lies within 2 standard deviations of the mean, and approximately 99.7% of the data lies within 3 standard deviations of the mean.

Step2: Answer part a

Since we want to find the percentage of healthy adults with body temperatures within 3 standard deviations of the mean, by the empirical rule, the percentage is 99.7.

Step3: Calculate the number of standard - deviations for part b

First, find the number of standard - deviations for the lower and upper bounds. Let $\mu = 98.39^{\circ}F$ and $\sigma=0.53^{\circ}F$. For the lower bound $x_1 = 97.33^{\circ}F$, the z - score $z_1=\frac{x_1 - \mu}{\sigma}=\frac{97.33 - 98.39}{0.53}=\frac{- 1.06}{0.53}=- 2$. For the upper bound $x_2 = 99.45^{\circ}F$, the z - score $z_2=\frac{x_2 - \mu}{\sigma}=\frac{99.45 - 98.39}{0.53}=\frac{1.06}{0.53}=2$. Since the data is within 2 standard deviations of the mean, by the empirical rule, the percentage of data within 2 standard deviations of the mean is 95.

Answer:

a. 99.7 b. 95