Suppose 1 is normally distributed with a mean of 3 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 8 and 10, respectively, find the mean and standard deviation of 1 2.

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

(c) Explain why 1 2 is normally distributed, despite the fact that both 1 and 2 are small.

(d) Suppose two independent samples are randomly obtained from populations 1 and 2, with sample sizes 1 = 8 and 2 = 10. Compute the probability that either sample average is at least 1 greater than the other.

Please show all calculations and explain how you got each calculation. I am so confused :(