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To answer this question, let’s analyze the details and use the **68-95-99.7 Rule** (also known as the empirical rule) in statistics. 

According to the problem:
- The mean body temperature (\(\mu\)) is \(98.4^\circ\)F.
- The standard deviation (\(\sigma\)) is \(0.8^\circ\)F.
  
The **68-95-99.7 Rule** tells us that:
- **68%** of data values fall within **1 standard deviation** of the mean (\(\mu \pm \sigma\)).
- **95%** of data values fall within **2 standard deviations** of the mean (\(\mu \pm 2\sigma\)).
- **99.7%** of data values fall within **3 standard deviations** of the mean (\(\mu \pm 3\sigma\)).

### Solution for Part (a)
We will calculate each option's interval based on these principles:

1. **Option A: 95% within ±2 standard deviations**
   - The interval will be: \(\mu \pm 2\sigma\)
   - Calculation:  
     \[
     98.4 \pm (2 \times 0.8) = 98.4 \pm 1.6
     \]
   - This gives the interval \( [98.4 - 1.6, 98.4 + 1.6] = [96.8, 100.0]\)

2. **Option B: 95% at least a certain temperature**
   - Since this is asking for a lower bound where 95% of temperatures are at or above, we look at the left tail of the distribution.
   - Since this is symmetric, 95% falls within ±2 standard deviations, so:
     \[
     98.4 - (2 \times 0.8) = 96.8^\circ \text{F}
     \]
   - Thus, about 95% of body temperatures are expected to be at least **96.8°F**.

3. **Option C: 95% less than a certain temperature**
   - This is asking for an upper bound where 95% of temperatures are at or below.
   - Similarly, using the +2 standard deviations:
     \[
     98.4 + (2 \times 0.8) = 100.0^\circ \text{F}
     \]
   - So, about 95% of body temperatures are expected to be **less than 100.0°F**.

### Final Answer:
- **Option A**: [96.8°F, 100.0°F]
- **Option B**: At least 96.8°F
- **Option C**: Less than 100.0°F

Would you like more details on this solution or have any questions?

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### Related Questions
1. How would the interval change if the standard deviation was different?
2. What does the 99.7% part of the 68-95-99.7 rule imply for body temperature?
3. How does changing the mean temperature affect these intervals?
4. What is the significance of using the normal distribution for body temperature?
5. Can you explain the differences between one-tail and two-tail in normal distribution analysis?

### Tip
When dealing with the 68-95-99.7 Rule, always identify the mean and standard deviation first; it simplifies calculations by letting you quickly determine intervals around the mean.

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 98.4°F. Furthermore, the standard deviation appeared to be around 0.8°F. Assume that a Normal model is appropriate. Complete parts a through c below. 
a) In what interval would you expect most people's body temperatures to be? Explain. Select the correct choice below and fill in the answer box(es) to complete your choice.

Learn how to calculate the interval for normal body temperatures using the 68-95-99.7 Rule. This problem involves a mean body temperature of 98.4°F with a standard deviation of 0.8°F, guiding students through understanding normal distribution and expected temperature intervals.

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