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Let's break down the solution to this question based on the 68-95-99.7 Rule (Empirical Rule) and the data provided.

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### Given Information:
- **Mean body temperature (µ)** = 97.9°F
- **Standard deviation (σ)** = 0.7°F

The 68-95-99.7 Rule tells us that for a normal distribution:
- About **68%** of values lie within **1 standard deviation** of the mean.
- About **95%** of values lie within **2 standard deviations** of the mean.
- About **99.7%** of values lie within **3 standard deviations** of the mean.

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### Part (a): Temperature Interval

Using the 68-95-99.7 Rule:
1. **68%** interval: Mean ± 1σ
   - \( 97.9 \pm 0.7 = [97.2, 98.6] \)
   
2. **95%** interval: Mean ± 2σ
   - \( 97.9 \pm 2 \times 0.7 = [96.5, 99.3] \)
   
3. **99.7%** interval: Mean ± 3σ
   - \( 97.9 \pm 3 \times 0.7 = [95.8, 100.0] \)

Since option **C** is selected, it correctly states that about **95% of body temperatures** are expected to be **between 96.5°F and 99.3°F**.

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### Part (b): Fraction Above 98.6°F

To find the fraction of people with body temperatures above 98.6°F:
1. **98.6°F** is **1 standard deviation above the mean** (97.9°F + 0.7°F).
2. From the Empirical Rule, about **16%** of the distribution lies above this point (since 68% is within ±1σ, leaving 32% outside this range, or 16% above +1σ).

So, **approximately 16%** of people would have body temperatures **above 98.6°F**.

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Would you like further details or clarification on any step? 

### Related Questions:
1. What is the significance of the Empirical Rule in statistics?
2. How does changing the standard deviation affect the interval estimates?
3. What is the probability of having a temperature below 96.5°F?
4. How would the intervals change if the mean temperature were higher?
5. Why is a normal distribution assumed in this analysis?

### Tip:
Remember, the Empirical Rule is useful for quick estimates in a normal distribution, but exact probabilities can be calculated with a Z-score table or statistical software.

Most people think that the 'normal' adult body temperature is 98.6°F. In a more recent study, researchers reported that a more accurate figure may be 97.9°F. Furthermore, the standard deviation appeared to be around 0.7°F. Assume that a Normal model is appropriate. Complete parts a and b below.

Learn how to calculate intervals for body temperatures using the Empirical Rule with a mean temperature of 97.9°F and standard deviation of 0.7°F. Understand how to determine the fraction of people expected to have temperatures above a specific threshold.

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