Compute all answers EDIT: A particular brand of dishwasher soap is sold in three

Question

Compute all answers

EDIT:

A particular brand of dishwasher soap is sold in three sizes: 25 oz, 30 oz, and 70 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 30-oz box, and the remaining 30% choose a 70-oz box. Let X1 and X2 denote the package sizes selected by two independently selected purchasers (a) Determine the sampling distribution of X 25 27.5 30 47.5 50 70 p(x) 04 12 X 06 X 06 X1/6 X 30 Calculate E(X) E(X)-41.67 Oz Compare E(X) to E(X) u (b) Determine the sampling distribution of the sample variance s2 s2 0 12.5 800 1012.5 p(s2) 1/4 1/4 1/4 1/4 Calculate E(s2) E(S2) 456.25

Explanation / Answer

a) P(X bar = 25) = 0.04

P(X bar = 27.5) = P(25,30) + P(30,25) = 2 * 0.2 * 0.5 = 0.2

P(X bar = 30) = P(30,30) = 0.5 * 0.5 = 0.25

P(X bar = 47.5) = P(25,70) + P(70,25) = 2 * 0.2 * 0.3 = 0.12

P(X bar = 50) = P(30,70) + P(70,30) = 2 * 0.5 * 0.3 = 0.3

P(X bar = 70) = P(70 , 70) = 0.3 * 0.3 = 0.09

b) P(s2 = 0) = P(25,25) + P(30,30) + P(70,70) = 0.2 * 0.2 + 0.5 * 0.5 + 0.3 * 0.3 = 0.38

P(s2 = 12.5) = P(25,30) + P(30,25) = 2 * 0.2 * 0.5 = 0.2

P(s2 = 800) = P(30,70) + P(70,30) = 2 * 0.5 * 0.3 = 0.3

P(s2 = 1012.5) = P(25,70) + P(70,25) = 2 * 0.2 * 0.3 = 0.12

E(s2) = 0 * 0.38 + 12.5 * 0.2 + 800 * 0.3 + 1012.5 * 0.12 = 364

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.