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To solve this problem, we need to construct a 98% confidence interval for the mean weight of all one-year-old baby boys in the United States. Here's the given information:

- Sample size (\(n\)) = 240
- Sample mean (\(\bar{x}\)) = 25.5 pounds
- Population standard deviation (\(\sigma\)) = 5.4 pounds
- Confidence level = 98%

### Step 1: Find the z-score for a 98% confidence level
The confidence level of 98% corresponds to a z-score of approximately 2.33 (from a standard normal distribution table).

### Step 2: Calculate the margin of error (E)
The formula for the margin of error is:

\[
E = z \times \frac{\sigma}{\sqrt{n}}
\]

Substituting the values:

\[
E = 2.33 \times \frac{5.4}{\sqrt{240}}
\]

### Step 3: Calculate the confidence interval
The confidence interval is calculated as:

\[
\text{Confidence interval} = \left( \bar{x} - E, \bar{x} + E \right)
\]

Let's now compute this step-by-step.

I'll calculate this for you:The 98% confidence interval for the mean weight of all one-year-old baby boys in the United States is approximately \( 24.7 \, \text{pounds} \leq \mu \leq 26.3 \, \text{pounds} \).

Would you like more details or have any questions?

Here are 5 related questions you could explore:
1. How does the sample size affect the width of a confidence interval?
2. What would happen to the confidence interval if the confidence level was increased to 99%?
3. How do you interpret the confidence interval in practical terms?
4. What is the relationship between the margin of error and the population standard deviation?
5. Can you calculate a confidence interval without knowing the population standard deviation?

**Tip:** Larger sample sizes lead to narrower confidence intervals, as they reduce the margin of error.

Construct a 98% confidence interval for the mean weight of all one-year-old baby boys in the United States. Sample size is 240, mean weight is 25.5 pounds, and the population standard deviation is 5.4 pounds.

This problem calculates a 98% confidence interval for the mean weight of one-year-old baby boys in the United States using a sample size of 240, with a mean weight of 25.5 pounds and a population standard deviation of 5.4 pounds.

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