Answered: A particular brand of dishwasher soap…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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$A particular brand of dishwasher soap is sold in three sizes: 30 oz, 40 oz, and 60 oz. Twenty percent of all purchasers select a 30-oz box, 50% choose a 40-oz box, and the remaining 30% choose a 60-oz box. Let $X_1$ and $X_2$ denote the package sizes selected by two independently selected purchasers. **(a) Determine the sampling distribution of $\bar{X}$.** - Table for $\bar{X}$: - $\bar{x}$: 30, 35, 40, 45, 50, 60 - $p(\bar{x})$: (empty fields to be filled by the user) - Calculate $E(\bar{X})$. - $E(\bar{X}) = $ (empty field for result) oz - Compare $E(\bar{X})$ to $\mu$. - Choices: - $E(\bar{X}) < \mu$ - $E(\bar{X}) = \mu$ - $E(\bar{X}) > \mu$ **(b) Determine the sampling distribution of the sample variance $S^2$.** - Table for $S^2$: - $s^2$: 0, 50, 200, 450 - $p(s^2)$: (empty fields to be filled by the user) - Calculate $E(S^2)$. - $E(S^2) = $ (empty field for result) - Compare $E(S^2)$ to $\sigma^2$. - Choices: - $E(S^2) = \sigma^2$ - $E(S^2) > \sigma^2$ - $E(S^2) < \sigma^2$$

Transcribed Image Text:A particular brand of dishwasher soap is sold in three sizes: 30 oz, 40 oz, and 60 oz. Twenty percent of all purchasers select a 30-oz box, 50% choose a 40-oz box, and the remaining 30% choose a 60-oz box. Let $X_1$ and $X_2$ denote the package sizes selected by two independently selected purchasers. **(a) Determine the sampling distribution of $\bar{X}$.** - Table for $\bar{X}$: - $\bar{x}$: 30, 35, 40, 45, 50, 60 - $p(\bar{x})$: (empty fields to be filled by the user) - Calculate $E(\bar{X})$. - $E(\bar{X}) = $ (empty field for result) oz - Compare $E(\bar{X})$ to $\mu$. - Choices: - $E(\bar{X}) < \mu$ - $E(\bar{X}) = \mu$ - $E(\bar{X}) > \mu$ **(b) Determine the sampling distribution of the sample variance $S^2$.** - Table for $S^2$: - $s^2$: 0, 50, 200, 450 - $p(s^2)$: (empty fields to be filled by the user) - Calculate $E(S^2)$. - $E(S^2) = $ (empty field for result) - Compare $E(S^2)$ to $\sigma^2$. - Choices: - $E(S^2) = \sigma^2$ - $E(S^2) > \sigma^2$ - $E(S^2) < \sigma^2$

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