Let X be the number of packages being mailed by a randomly selected customer at a shipping facility. Suppose the distribution of X is as follows: 1 X 2 3 4 P(x) .4 .3 .2. .1 a. Consider a random sample of size n = 2 and let X be the sample mean number of mails delivered. Obtain the probability distribution of X. b. Refer to part (a) and calculate P(X 2.5). c. If a random sample of size n-4 is selected, what is P(X 1.5)? d. Consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R.