Financial Risk Manager Part 1

The mean is 85, the standard deviation is 18, and the sample size is 40.

The 99% z-value is 2.58.

Confidence interval = $\bar{x} \pm z^* \left(\frac{\sigma}{\sqrt{n}}\right)$

= $85 \pm 2.58 \left(\frac{18}{\sqrt{40}}\right) = [77.658; 92.342]$

Calculation breakdown:

• Standard error = $\frac{18}{\sqrt{40}} = \frac{18}{6.3246} = 2.846$
• Margin of error = $2.58 \times 2.846 = 7.342$
• Lower bound = $85 - 7.342 = 77.658$
• Upper bound = $85 + 7.342 = 92.342$

Therefore, the 99% confidence interval is [77.658; 92.342].