A particular brand of dishwasher soap is sold in three sizes 25 oz, 40 oz, and 7

Question

A particular brand of dishwasher soap is sold in three sizes 25 oz, 40 oz, and 70 oz. Twenty percent of all purchasers select a 25 oz box, 50% select a 40 oz box, and the remaining 30% choose a 70-oz box. Let X_1 and X_2 denote the package sizes selected by two independently selected purchasers. Determine the sampling distribution of X bar. Calculate E(X) bar E(X) bar=oz Compare E(X)bar to mu Determine the sampling distribution of the sample variance S^2. Calculate E(S^2). E(S^2) = Compare E(S^2) to sigma^2.

Explanation / Answer

b) from above

summing up duplicate values:

E(S2) =350

X1 X2 S^2 P(S^2) 25 25 0 1/9 40 25 112.5 1/9 70 25 1012.5 1/9 25 40 112.5 1/9 40 40 0 1/9 70 40 450 1/9 25 70 1012.5 1/9 40 70 450 1/9 70 70 0 1/9

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