Financial Risk Manager Part 1

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