A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 60 oz. Twenty percent of all purchasers select a 35-oz box, 50% select a 40-oz box, and the remaining 30% choose a 60-oz box. Let X1 and X2 denote the package sizes selected by two independently selected purchasers.
a. Determine the sampling distribution of X.
b. Determine the sampling distribution of the sample variance S^2.
