In: Math
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.
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 |