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To construct a 99% confidence interval for the true population mean textbook weight (\(\mu\)), given the sample data, we can use the formula for a confidence interval when the population standard deviation is known:

\[
\text{Confidence Interval} = \bar{x} \pm z \cdot \frac{\sigma}{\sqrt{n}}
\]

where:
- \(\bar{x}\) is the sample mean,
- \(z\) is the z-score corresponding to the confidence level,
- \(\sigma\) is the population standard deviation, and
- \(n\) is the sample size.

### Given Data
- Sample mean \(\bar{x} = 72\) ounces
- Population standard deviation \(\sigma = 5.9\) ounces
- Sample size \(n = 30\)
- Confidence level = 99%

### Step 1: Find the z-score
For a 99% confidence level, the z-score is approximately \(2.576\) (you can find this value from the z-table).

### Step 2: Calculate the Standard Error (SE)
The standard error is given by:
\[
\text{SE} = \frac{\sigma}{\sqrt{n}} = \frac{5.9}{\sqrt{30}} \approx 1.077
\]

### Step 3: Calculate the Margin of Error (ME)
\[
\text{ME} = z \cdot \text{SE} = 2.576 \cdot 1.077 \approx 2.774
\]

### Step 4: Construct the Confidence Interval
\[
\text{Confidence Interval} = \bar{x} \pm \text{ME} = 72 \pm 2.774
\]
This gives:
\[
69.23 < \mu < 74.77
\]

### Answer
The 99% confidence interval for the true population mean textbook weight is:

\[
69.23 < \mu < 74.77
\]

Would you like more details or have any questions about this process?

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Here are 5 related questions that can deepen your understanding:

1. How would the confidence interval change if we increased the sample size?
2. Why do we use a z-score for confidence intervals instead of a t-score in this case?
3. What would the interval look like for a 95% confidence level instead of 99%?
4. How does the population standard deviation affect the width of the confidence interval?
5. What happens to the confidence interval if the sample mean is slightly different, say 73 ounces?

**Tip:** Remember, the confidence interval width depends on both the sample size and the level of confidence. Higher confidence levels lead to wider intervals.

You measure 30 randomly selected textbooks' weights, and find they have a mean weight of 72 ounces. Assume the population standard deviation is 5.9 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places.

Calculate a 99% confidence interval for the mean textbook weight given a sample mean of 72 ounces, a population standard deviation of 5.9 ounces, and a sample size of 30. This solution explains each step of the confidence interval calculation process.

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