In order to calculate the confidence interval, we can use the formula below:
[tex]CI=\mu\pm z\cdot\frac{\sigma}{\sqrt{n}}[/tex]For an interval with a confidence of 99%, we need to use z = 2.576.
Then, using a mean of 85.6, a standard deviation of 2.9 and a sample size of 52, we have:
[tex]\begin{gathered} CI=85.6\pm2.576\cdot\frac{2.9}{\sqrt{52}}\\ \\ CI=85.6\pm2.576\cdot0.4021576\\ \\ CI=85.6\pm1.036\\ \\ CI=(84.564,86.636) \end{gathered}[/tex]