Questions: The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.35°F and a standard deviation of 0.56°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 97.79°F and 98.91°F? b. What is the approximate percentage of healthy adults with body temperatures between 97.23°F and 99.47°F?

Solution Steps

The empirical rule states that for a bell-shaped distribution (normal distribution):

• Approximately \(68\%\) of the data falls within 1 standard deviation (\(\sigma\)) of the mean (\(\mu\)).
• Approximately \(95\%\) of the data falls within 2 standard deviations of the mean.
• Approximately \(99.7\%\) of the data falls within 3 standard deviations of the mean.

Given:

• Mean (\(\mu\)) = \(98.35^{\circ} \mathrm{F}\)
• Standard deviation (\(\sigma\)) = \(0.56^{\circ} \mathrm{F}\)
• Range: \(97.79^{\circ} \mathrm{F}\) to \(98.91^{\circ} \mathrm{F}\) (which is \(\mu - \sigma\) to \(\mu + \sigma\)).

Using the empirical rule, the percentage of healthy adults within this range is approximately \(68\%\).

Given:

• Range: \(97.23^{\circ} \mathrm{F}\) to \(99.47^{\circ} \mathrm{F}\) (which is \(\mu - 2\sigma\) to \(\mu + 2\sigma\)).

Using the empirical rule, the percentage of healthy adults within this range is approximately \(95\%\).

Final Answer