Answer: [41.6 days; 48.4 days]

## Explanation To calculate the 95% confidence interval for the population mean, we use the formula: **Confidence Interval = Sample Mean ± (Z-value × Standard Error)** ### Step 1: Calculate Standard Error Standard Error = σ / √n = 19 / √121 = 19 / 11 = 1.7273 ≈ 1.73 ### Step 2: Identify Z-value For a 95% confidence interval, the Z-value is 1.96 ### Step 3: Calculate Margin of Error Margin of Error = Z-value × Standard Error = 1.96 × 1.73 = 3.3908 ≈ 3.4 ### Step 4: Calculate Confidence Interval Lower Limit = 45 - 3.4 = 41.6 days Upper Limit = 45 + 3.4 = 48.4 days Therefore, the 95% confidence interval is **[41.6 days; 48.4 days]** **Key Points:** - We use Z-distribution because the population is normally distributed - Sample size (n=121) is sufficiently large - Standard error decreases with larger sample sizes - The confidence interval represents the range where we're 95% confident the true population mean lies

Author: Tanishq Prabhu