To solve this problem using the empirical rule (68-95-99.7 rule):

Given:

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

Part 1: a.

• The temperatures between $97.65$°F and $98.87$°F are within $1$ standard deviation of the mean.
• By the empirical rule, approximately 68% of the data lies within 1 standard deviation of the mean.

Thus, the approximate percentage is 68%.

Part 2: b.

• The temperatures between $96.43$°F and $100.09$°F are within $3$ standard deviations of the mean.

Calculations: $\text{Lower bound} = \mu - 3\sigma = 98.26 - 3(0.61) = 96.43 \text{°F}$ $\text{Upper bound} = \mu + 3\sigma = 98.26 + 3(0.61) = 100.09 \text{°F}$

• By the empirical rule, approximately 99.7% of the data lies within 3 standard deviations of the mean.

So, the approximate percentage is 99.7%.

Would you like more details or have any other questions?

Here are some related questions:

1. What percentage of data lies within 2 standard deviations of the mean?
2. What is the z-score and how is it related to the empirical rule?
3. How would the percentages change if the distribution were not normal?
4. What other statistical methods can be used to describe the spread of data?
5. How do you calculate the exact percentage using the standard normal distribution?

Tip: The empirical rule is a quick way to estimate the spread of data in a normal distribution, but for more precise results, using z-scores and the standard normal table is more accurate.