Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. x | 1 2 3 4

p(x) | 0.4 0.3 0.2 0.1

Required:
a. Consider a random sample of size n=2 (two customers), and let Xbar be the sample mean number of packages shipped. Obtain the probability distribution of Xbar.
b. Use (a) to calculate P (Xbar <= 2.5).
c. If a random sample of size 4 is selected, what is P (Xbar <= 1.5)? (Hint: don't list all possible outcomes; only those for which xbar <= 1.5).
d. Find V(Xbar)