. Suppose 1 is normally distributed with a mean of 4 and a standard deviation of 1 and suppose 2 is normally distributed with a mean of 5 and a standard deviation of 2.

(a) For independent samples of sizes 9 and 16, respectively, find the mean and standard deviation of 1 2. (3 marks)

(b) Would your answers in (a) change if 1 and/or 2 were not normally distributed? Explain your answer. (2 marks)

(c) Explain why 1 2 is normally distributed, even though both 1 and 2 are small. (2 marks)

(d) Suppose two independent samples are randomly obtained from populations 1 and 2, with sample sizes 1 = 9 and 2 = 16. Compute the probability that either sample average is at least 2 greater than the other. (6 marks)