Question

A particular brand of dishwasher soap is sold in three sizes: 35 02, 40 oz, and 70 02. Twenty percent of all purchasers select a 35-oz box, 50% select a 40-oz box, and the remaining 30% choose a 70 oz box. Let X, and X, denote the package sizes selected by two independently selected purchasers. (a) Determine the sampling distribution of X. 35 37.5 40 52.5 P(x) Calculate E(X) E(X) = Compare E(Xto . EX) = EXO < EX>

Answer 1

a)below is distribution of xbar:

X1	x2	xbar	P(x1,x2)
35	35	35	0.04
40	35	37.5	0.1
70	35	52.5	0.06
35	40	37.5	0.1
40	40	40	0.25
70	40	55	0.15
35	70	52.5	0.06
40	70	55	0.15
70	70	70	0.09

from above :

xbar	35	37.5	40	52.5	55	70
p(xbar)	0.04	0.2	0.25	0.12	0.3	0.09

E(Xbar)=48

E(Xbar)=μ

b)

s^2	0	12.5	450	612.5
p(s^2)	0.38	0.2	0.3	0.12

E(s²) =211

E(s²) = σ²