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Let's solve the problem by finding the 95% confidence interval for the true mean waiting time.

### Given:
- Sample mean (\(\bar{x}\)) = 9.3 minutes
- Standard deviation (\(s\)) = 6.2 minutes
- Sample size (\(n\)) = 200 passengers
- Confidence level = 95%

### Steps:
1. **Identify the z-score** for a 95% confidence level. The critical value \(z_{\alpha/2}\) for 95% confidence is approximately **1.96** (from the standard normal distribution table).

2. **Calculate the standard error (SE)**:
   \[
   SE = \frac{s}{\sqrt{n}} = \frac{6.2}{\sqrt{200}} \approx \frac{6.2}{14.14} \approx 0.4383
   \]

3. **Compute the margin of error (ME)**:
   \[
   ME = z_{\alpha/2} \times SE = 1.96 \times 0.4383 \approx 0.858
   \]

4. **Determine the confidence interval**:
   - Lower limit = \(\bar{x} - ME = 9.3 - 0.858 = 8.442\)
   - Upper limit = \(\bar{x} + ME = 9.3 + 0.858 = 10.158\)

Thus, the 95% confidence interval is approximately **(8.4, 10.2)**.

The correct answer is **B: 8.4 and 10.2**.

Would you like more details or explanations on any part of this calculation?

### Related Questions:
1. What is the formula for calculating the confidence interval for a population mean?
2. How do you interpret a 95% confidence interval?
3. How does the sample size affect the width of the confidence interval?
4. What assumptions must be satisfied to use the z-score in confidence intervals?
5. What is the impact of changing the confidence level from 95% to 99%?

### Tip:
Always ensure your sample size is large enough to assume a normal distribution when calculating confidence intervals, especially if the population standard deviation is unknown.

A study conducted by a commuter train transportation authority involved surveying a random sample of 200 passengers. The results show that a customer had to wait on average 9.3 minutes with a standard deviation of 6.2 minutes to buy his or her ticket. Assuming a Normal distribution, lower and upper limits of the 95% confidence interval of the true mean waiting time are respectively?

Learn how to calculate the 95% confidence interval for the mean waiting time in a commuter train study. This problem involves key statistical concepts like the normal distribution, confidence intervals, and the use of the z-score. Suitable for students in Grades 10-12.

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