A particular brand of dishwasher soap is sold in three sizes: 25 oz, 30 oz, and 65 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 30-oz box, and the remaining 30% choose a 65- oz box. Let X, and X, denote the package sizes selected by two independently selected purchasers. (a) Determine the sampling distribution of X. X 25 27.5 30 45 47.5 65 p(x) 0.04 Calculate E(X). E(X) = OZ Compare E(X) to u. O E(X) = M O E( X ) M (b) Determine the sampling distribution of the sample variance $2. 0 12.5 612.5 800 p (52 ) Calculate E($2). E(S2) = Compare E(S2) to 62. O E(S2) 62 O E(S2) = 62