Question

In: Math

A particular brand of dishwasher soap is sold in three sizes: 30 oz, 45 oz, and...

A particular brand of dishwasher soap is sold in three sizes: 30 oz, 45 oz, and 65 oz. Twenty percent of all purchasers selec

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

Solutions

Expert Solution

sampling distribution of mean is as follows":

x1 x2 P(x1,x2) 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

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