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 X1, X2, X3, X4, and X, be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with – 112 – 20, l3 - MA – Ms – 24, and of – o – 4 for the economy brand and ož = o = of = 3,5 for the name brand. Define the rv Y by X1+ Xg_ X3 + X4 + Xg Y = 3 so that Y is a measure of the difference in efficiency between economy gas and name-brand gas. Compute oy .[3 decimal places]
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 X1, X2, X3, X4, and X, be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with – 112 – 20, l3 - MA – Ms – 24, and of – o – 4 for the economy brand and ož = o = of = 3,5 for the name brand. Define the rv Y by X1+ Xg_ X3 + X4 + Xg Y = 3 so that Y is a measure of the difference in efficiency between economy gas and name-brand gas. Compute oy .[3 decimal places]
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]**
\[
\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae8ee7c4-79f3-4258-9a28-9911a1447d64%2F970eb9ff-42bc-4a61-9a84-7aa9a408df8d%2Fntxiy9n_processed.png&w=3840&q=75)
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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