Question

particular brand of dishwasher soap is sold in three sizes: 35 oz, 40 oz, and 60 oz. Twenty percent of all purchasers select a 35-oz box, 50% select a 40-oz box, and the remaining 30% choose a 60-oz box. Let X₁ and X₂ denote the package sizes selected by two independently selected purchasers.

(a) Determine the sampling distribution of

X.

x	35	37.5	40	47.5	50	60
p(x)

Calculate

E(X).

E(X) =

oz

Compare

E(X)

to μ.

E(X) > μ

E(X) = μ

    

E(X) < μ

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

s2	0	12.5	200	312.5
p(s2)

Calculate E(S²).
E(S²) =

Compare E(S²) to σ².

E(S²) = σ²

E(S²) > σ²

    

E(S²) < σ²

Answer 1

a) from given data"

xbar	35	37.5	40	47.5	50	60
p(xbar)	0.04	0.2	0.25	0.12	0.3	0.09

E(X)=xP(x) =45

E(x̅)=μ

b)

s^2	0	12.5	200	312.5
p(s^2)	0.38	0.2	0.3	0.12

E(s²)=s²P(s²) =45

E(S²) = σ²