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A particular brand of dishwasher soap is sold in three sizes: 30 oz, 45 oz, and 65 oz. Twenty percent of all purchasers select a 30-oz box, 50% select a 45-oz box, and the remaining 30% choose a 65-oz box. Let X_{1} and X_{2} denote the package sizes selected by two independently selected purchasers.
(a) Determine the sampling distribution of X. x 30 37.5 45 47.5 55 65 p(x) Calculate E(X). E(X) = oz Compare E(X) to µ. E(X) > µ E(X) < µ E(X) = µ.
(b) Determine the sampling distribution of the sample variance S^{2}. s^{2} 0 112.5 200 612.5 p(s^{2}) Calculate E(S^{2}). E(S^{2}) = Compare E(S^{2}) to s^{2}. E(S^{2}) < s^{2} E(S^{2}) = s^{2} E(S^{2}) > s^{2}.
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