Financial Risk Manager Part 1

The correct answer is A. The confidence interval is calculated using the formula:

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

Where:

• $\bar{x} = 85$ (sample mean)
• $\sigma = 18$ (population standard deviation)
• $n = 40$ (sample size)
• $z^* = 2.58$ (z-value for 99% confidence level)

Calculation: $`$85 \pm 2.58\left(\frac{18}{\sqrt{40}}\right)$$ $85` \pm 2.58\left(\frac{18}{6.3246}\right)$$ $85 \pm 2.58(2.846) $`$85` \pm 7.342

Therefore, the confidence interval is: $[85 - 7.342; 85 + 7.342] = [77.658; 92.342]$

This matches option A. Option B has an incorrect lower bound, option C has an incorrect upper bound, and option D uses different values that don't match the calculation.