Answer: [14.4 miles; 21.6 miles]

## Explanation To calculate the 99% confidence interval for the population mean, we use the formula: **Confidence Interval = Sample Mean ± (Z-score × Standard Error)** ### Step 1: Calculate Standard Error Standard Error = $\frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}} = \frac{14}{\sqrt{100}} = \frac{14}{10} = 1.4$ ### Step 2: Find Z-score for 99% Confidence Level For a 99% confidence interval, the Z-score (reliability factor) is 2.58 ### Step 3: Calculate Margin of Error Margin of Error = Z-score × Standard Error = 2.58 × 1.4 = 3.612 ### Step 4: Calculate Confidence Interval - Lower Limit = Sample Mean - Margin of Error = 18 - 3.612 = 14.388 ≈ 14.4 miles - Upper Limit = Sample Mean + Margin of Error = 18 + 3.612 = 21.612 ≈ 21.6 miles Therefore, the 99% confidence interval is **[14.4 miles; 21.6 miles]** **Key Points:** - We use Z-distribution because the population standard deviation is known - The sample size (n=100) is sufficiently large - The confidence interval represents the range where we are 99% confident the true population mean lies

Author: Tanishq Prabhu