Question

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, and X2 denote the package sizes selected by two independently selected purchasers 

(a) Determine the sampling distribution of X. 

(b) Determine the sampling distribution of the sample variance S². 

Answer 1

sampling distribution of mean is as follows":

x1	x2	P(x1,x2)	x̅	s2
30	30	0.04	30	0
45	30	0.10	37.5	112.5
65	30	0.06	47.5	612.5
30	45	0.10	37.5	112.5
45	45	0.25	45	0
65	45	0.15	55	200
30	65	0.06	47.5	612.5
45	65	0.15	55	200
65	65	0.09	65	0

a)

xbar	30	37.5	45	47.5	55	65
p(xbar)	0.04	0.2	0.25	0.12	0.3	0.09

E(x̅)=	48
E(x̅)=μ

b)

s^2	0	112.5	200	612.5
p(s^2)	0.38	0.2	0.3	0.12

E(s2) =	156
E(s2) =σ2