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To construct a 99% confidence interval estimate of the mean body temperature for all healthy humans, we can follow these steps:

### Given Information
- Sample mean (\(\bar{x}\)) = 98.0°F
- Standard deviation (\(s\)) = 0.74°F
- Sample size (\(n\)) = 110
- Confidence level = 99%

### Step 1: Find the Z-score for a 99% Confidence Level
For a 99% confidence level, the Z-score corresponding to the upper tail (0.5% on each side for a two-tailed test) is approximately **2.576**.

### Step 2: Calculate the Standard Error of the Mean (SEM)
The standard error of the mean is calculated by:
\[
\text{SEM} = \frac{s}{\sqrt{n}} = \frac{0.74}{\sqrt{110}}
\]
Calculating this gives:
\[
\text{SEM} \approx \frac{0.74}{10.4881} \approx 0.0705
\]

### Step 3: Calculate the Margin of Error (ME)
The margin of error is calculated by multiplying the Z-score with the standard error:
\[
\text{ME} = Z \times \text{SEM} = 2.576 \times 0.0705 \approx 0.1816
\]

### Step 4: Construct the Confidence Interval
Now, we add and subtract the margin of error from the sample mean to find the confidence interval:
\[
\text{Lower bound} = \bar{x} - \text{ME} = 98.0 - 0.1816 \approx 97.8184
\]
\[
\text{Upper bound} = \bar{x} + \text{ME} = 98.0 + 0.1816 \approx 98.1816
\]

### Final Answer
The 99% confidence interval for the mean body temperature is:
\[
97.818 < \mu < 98.182
\]

### Interpretation
This interval does not include the traditional average of 98.6°F, suggesting that the true average body temperature of healthy adults might be lower than 98.6°F.

Would you like more details on any of these steps? 

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Here are some related questions:
1. How is the Z-score for a confidence interval determined?
2. What is the difference between Z-scores and t-scores in confidence intervals?
3. How does sample size impact the margin of error?
4. Why might 98.6°F not be the true mean body temperature?
5. How does confidence level affect the width of a confidence interval?

**Tip:** The margin of error decreases as the sample size increases, making estimates more precise.

A data set includes 110 body temperatures of healthy adult humans having a mean of 98.0°F and a standard deviation of 0.74°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature?

Construct a 99% confidence interval estimate for the mean body temperature of healthy adults, using a sample mean of 98.0°F and standard deviation of 0.74°F based on 110 samples. Explore how this interval compares to the traditional average body temperature of 98.6°F.

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