The problem involves a bell-shaped distribution (which is a normal distribution) and uses the empirical rule (68-95-99.7 rule) to estimate percentages of data within certain ranges of standard deviations from the mean.

Given:

• Mean $\mu = 98.26$°F
• Standard deviation $\sigma = 0.61$°F

a. To find the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, between $\mu - 1\sigma$ and $\mu + 1\sigma$, we calculate:

$\mu - 1\sigma = 98.26 - 0.61 = 97.65 \text{°F}$

$\mu + 1\sigma = 98.26 + 0.61 = 98.87 \text{°F}$

Using the empirical rule:

• Approximately 68% of the data falls within 1 standard deviation of the mean in a normal distribution.

So, the approximate percentage is 68%.

b. For temperatures between 96.43°F and 100.09°F, first, let's determine how many standard deviations these values are from the mean:

$96.43 \text{°F} = \mu - 3\sigma = 98.26 - 3(0.61)$ $100.09 \text{°F} = \mu + 3\sigma = 98.26 + 3(0.61)$

The empirical rule tells us:

• About 99.7% of data falls within 3 standard deviations of the mean.

So, the approximate percentage is 99.7%.

Do you want any additional details or have any questions?

Here are some related questions:

1. What is the percentage of data within 2 standard deviations of the mean?
2. How does the empirical rule apply to non-normal distributions?
3. How do you calculate percentages for data more than 3 standard deviations away from the mean?
4. How can you use the z-score in normal distribution calculations?
5. What are some real-world examples where the empirical rule is used?

Tip: Always remember, the empirical rule is specifically for normal distributions. It may not apply to skewed or other non-normal distributions.