Hello, I have two questions shown in the image below that I need help with explaining

For 1. Let X1, X2,....Xn, be a random sample from a population with the same exponential distribution. Find the distribution of sample mean.

- For this, I tried to based it on the central limit theorem. Is that the right approach?

(2 points) Let X1, X2, ..., Xn be a random sample from a population with the same exponential distribution. Find the distribution of sample mean. (2 points) Let X1,X2, ...,Xn be a random sample from a population with the normal distribution with a\" = 3. If a samples size n = 25 is randomly selected, nd the probability that the sample mean will be within 0.57 of the true mean, ,u