Question

The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.08°F and a standard deviation of 0.43°F. Using the empirical rule, find each approximate percentage below 

a. What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.65°F and 98.51°F? 

b. What is the approximate percentage of healthy adults with body temperatures between 97 22°F and 98.94°F? 

a. Approximately _______ % of healthy adults in this group have body temperatures within 1 standard deviation of the mean, or between 9765°F and 98.51°F. 

b. Approximately _______ % of healthy adults in this group have body temperatures between 97.22°F and 98.94°F.

Answer 1

Given body temperatures have a bell shaped distribution with mean \(\mu=98.08 \mathrm{~F}\)

Standard deviation \(\sigma=0.43 \mathrm{~F}\)

a) \(P(97.65

$$ \begin{aligned} &=P(-1 < Z< 1) \\ &=0.68 \quad \text { \{usingempirical rule\} } \end{aligned} $$

Approximately \(68 \%\) of adults in the group have body temperatures within 1 SD

b) \(\mathrm{P}(97.22<\mathrm{X}<98.94)=\mathrm{P}\left(\frac{97.22-98.08}{0.43}<\frac{x-\mu}{\sigma}<\frac{98.94-98.09}{0.43}\right)\)

$$ \begin{aligned} &=\mathrm{P}(-2<\mathrm{z}<2) \\ &=0.95 \quad \text { \{usingempirical rule\} } \end{aligned} $$

Approximately \(95 \%\) of adults in the group have body temperatures between \(97.22\) and \(98.94\)