3. A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. Let X₁ and X2 denote the package sizes selected by two independently selected purchasers. (a) Determine the sampling distribution of X (the mean of X₁ and X2). (b) Calculate E(X), and compare to population mean μ, the mean size of a randomly selected soap. (c) Calculate var(X), and compare to σ²/n, where σ² is the popula- tion variance (variance of the size of a randomly selected soap).
3. A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. Let X₁ and X2 denote the package sizes selected by two independently selected purchasers. (a) Determine the sampling distribution of X (the mean of X₁ and X2). (b) Calculate E(X), and compare to population mean μ, the mean size of a randomly selected soap. (c) Calculate var(X), and compare to σ²/n, where σ² is the popula- tion variance (variance of the size of a randomly selected soap).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:3. A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40
oz, and 65 oz. Twenty percent of all purchasers select a 25-oz box, 50%
select a 40-oz box, and the remaining 30% choose a 65-oz box. Let X₁
and X2 denote the package sizes selected by two independently selected
purchasers.
(a) Determine the sampling distribution of X (the mean of X₁ and
X2).
(b) Calculate E(X), and compare to population mean μ, the mean
size of a randomly selected soap.
(c) Calculate var(X), and compare to σ²/n, where σ² is the popula-
tion variance (variance of the size of a randomly selected soap).
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