2. (20 points) Suppose that we have two random samples. The first sample has size n =64 and is drawn from a normal population with population mean = 3 and population standard deviation o = 3. The second sample has size n2 = 25 and is drawn from a normal population with population mean 2 = 10 and population standard deviation = 7. Let X, and S7, i=1,2, denote the sample average and sample standard deviation, respectively, of the ith sample. (a) State the sampling distribution of the following quantities: i. X2 ii. (n-1)/0 iii. (S)/(0) (b) Find the probability that S exceeds 47.646.