Answered: Five automobiles of the same type are…

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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$Five automobiles of the same type are to be driven on a 300-mile trip. The first two will use an economy brand of gasoline, and the other three will use a name brand. Let $X_1, X_2, X_3, X_4,$ and $X_5$ be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with $\mu_1 = \mu_2 = 20$, $\mu_3 = \mu_4 = \mu_5 = 24$, and $\sigma_1^2 = \sigma_2^2 = 4$ for the economy brand and $\sigma_3^2 = \sigma_4^2 = \sigma_5^2 = 3.5$ for the name brand. Define the random variable $Y$ by \[ Y = \frac{X_1 + X_2}{2} - \frac{X_3 + X_4 + X_5}{3} \] so that $Y$ is a measure of the difference in efficiency between economy gas and name-brand gas. **Compute $\sigma_Y$. [3 decimal places]** \[ \text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_} \]$

Transcribed Image Text:Five automobiles of the same type are to be driven on a 300-mile trip. The first two will use an economy brand of gasoline, and the other three will use a name brand. Let $X_1, X_2, X_3, X_4,$ and $X_5$ be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with $\mu_1 = \mu_2 = 20$, $\mu_3 = \mu_4 = \mu_5 = 24$, and $\sigma_1^2 = \sigma_2^2 = 4$ for the economy brand and $\sigma_3^2 = \sigma_4^2 = \sigma_5^2 = 3.5$ for the name brand. Define the random variable $Y$ by \[ Y = \frac{X_1 + X_2}{2} - \frac{X_3 + X_4 + X_5}{3} \] so that $Y$ is a measure of the difference in efficiency between economy gas and name-brand gas. **Compute $\sigma_Y$. [3 decimal places]** \[ \text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_} \]

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