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To solve this problem, we are asked to construct a 99% confidence interval for the true population mean textbook weight (\(\mu\)) based on the given data.

### Step-by-step solution:

1. **Given dataTo solve this problem, we are asked to construct a 99% confidence interval for the true population mean textbook weight (\(\mu\)) based on the given data.

### Step-by-step solution:

1. **Given **
   - Sample mean (\(\bar{x}\)) = 60 ounces
   - Population standard deviation (\(\sigma\)) = 4.9 ounces
   - Sample size (\(n\)) = 42
   - Confidence level = 99%

2. **Confidence interval formula:**
   The confidence interval for the population mean when the population standard deviation is known is given by:
   \[
   \bar{x} \pm z_{\alpha/2} \cdot \left(\frac{\sigma}{\sqrt{n}}\right)
   \]
   where:
   - \(\bar{x}\) = sample mean
   - \(\sigma\) = population standard deviation
   - \(n\) = sample size
   - \(z_{\alpha/2}\) = z-value corresponding to the confidence level (for 99%, \(z_{\alpha/2} = 2.576\))

3. **Calculate the margin of error:**
   The margin of error is:
   \[
   E = z_{\alpha/2} \cdot \left(\frac{\sigma}{\sqrt{n}}\right)
   \]
   Substituting the values:
   \[
   E = 2.576 \cdot \left(\frac{4.9}{\sqrt{42}}\right)
   \]

Let's calculate the margin of error and the confidence interval.It seems like I can’t do more advanced data analysis right now. Please try again later. 

Would you like me to guide you through the calculation steps, or is there anything else you need help with? Let me know if you'd like a different approach.

Here are 5 related questions that could extend your understanding:
1. How is the z-value for a confidence interval chosen, and why is it different for various confidence levels?
2. How does the sample size affect the width of a confidence interval?
3. What is the difference between a confidence interval and a margin of error?
4. How would the confidence interval change if the standard deviation was higher or lower?
5. What would happen if we had to use the t-distribution instead of the normal distribution?

**Tip:** The confidence interval widens as the confidence level increases, meaning higher confidence requires a wider range.

You measure 42 textbooks' weights, and find they have a mean weight of 60 ounces. Assume the population standard deviation is 4.9 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.

Calculate the 99% confidence interval for the mean weight of textbooks, given a sample mean of 60 ounces, population standard deviation of 4.9 ounces, and sample size of 42. Explore key statistical concepts such as the z-score and margin of error.

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