Aparticular brand of dishwasher soap is sold in three sizes: 25 oz, 45 oz, and 60 oz. twenty percent of all purchasers select a 25-oz box, 50% select a 45-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 25 35 45 42.5 52.5 60 p(x) calculate e(x). e(x) = oz compare e(x) to μ. e(x) > μ e(x) < μ e(x) = μ

(a) Sampling distribution

P(25) = 0,04

P(35) = 0.1 + 0.1 = 0,2

P(42,5) = 0.06 + 0.06 = 0,12

P(45) = 0,25

P(52,5) = 0.15 + 0.15 = 0,3

P(60) = 0,09

(b) E(X) = 45.5 oz

(c) E(X) = μ

Step-by-step explanation:

The variable we want to compute is

For this we need to know all the possible combinations of X1 and X2 and the probability associated with them.

(a) Sampling distribution

Calculating all the 9 combinations (3 repeated, so we end up with 6 unique combinations):

P(25) = P(X1=25) * P(X2=25) = p25*p25 = 0.2 * 0.2 = 0,04

P(35) = p25*p45+p45*p25 = 0.2*0.5 + 0.5*0.2 = 0.1 + 0.1 = 0,2

P(42,5) = p25*p60 + p60*p25 = 0.2*0.3 + 0.3*0.2 = 0.06 + 0.06 = 0,12

P(45) = p45*p45 = 0.5 * 0.5 = 0,25

P(52,5) = p45*p60 + p60*p45 = 0.5*0.3 + 0.3*0.5 = 0.15 + 0.15 = 0,3

P(60) = p60*p60 = 0.3*0.3 = 0,09

(b) Using the sample distribution, E(X) can be expressed as:

The value of E(X) is 45.5 oz.

(c) The value of μ can be calculated as

We can conclude that E(X)=μ

We could have arrived to this conclusion by applying

a. the residual plot for model 1 has a random pattern and is a good fit for the data.

step-by-step explanation:

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