The confidence interval extremities are given by the formula:
m +/- (z · σ / √n)
In your problem:
m = 3.13
σ = 0.23
n = 36
The z-score for a 99% confidence interval is 2.576
Therefore:
m - (z · σ / √n) = 3.13 - (2.576 · 0.23 / √36) = 3.031
m + (z · σ / √n) = 3.13 + (2.576 · 0.23 / √36) = 3.229
Therefore, the confidence interval is (3.031, 3.229).