I need proper solution and step by step with full explanation and curve Neat and clean please

Question 2. A camp director is interested in the mean number of letters each child sends during his or her camp session. A survey of 25 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8. (Please show all formulas, calculations and the curve) (a) Find a 95% confidence interval for the mean number of letters each child sends during the camp session. Interpret this confidence intervals. (b) Suppose that the population standard deviation of 3 is given. If you wanted to estimate the mean number of letters each child sends during the camp session with 90% confidence, and a margin of error of 0.25, how large a sample would you need