Answer: [77.658; 92.342]

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.

Author: Nikitesh Somanthe