Let X be the number of packages being mailed by a ran- domly selected customer at a certain shipping facility. Suppose the distribution of X is as follows: x p(x) 1 2 3 4 4 3 2 1

a. Consider a random sample of size n = 2 (two cus- tomers), and let X be the sample mean number of pack- ages shipped. Obtain the probability distribution of X.

b. Refer to part

(a) and calculate P(X 2.5).

c. Again 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. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]

d. If a random sample of size n = 4 is selected, what is PX1.5)? [Hint: You should not have to list all pos- sible outcomes, only those for which 1.5.]