Solution Found!
A gas station earns $2.60 in revenue for each gallon of
Chapter 2, Problem 10E(choose chapter or problem)
A gas station earns $2.60 in revenue for each gallon of regular gas it sells, $2.75 for each gallon of midgrade gas, and $2.90 for each gallon of premium gas. Let \(X_1\), \(X_2\), and \(X_3\) denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that \(X_1\), \(X_2\), and \(X_3\) have means \(\mu_1=1500\), \(\mu_2=500\), and \(\mu_3=300\), and standard deviations \(\sigma_1=180\), \(\sigma_2=90\), and \(\sigma_3=40\), respectively.
a. Find the mean daily revenue.
b. Assuming \(X_1\), \(X_2\), and \(X_3\) to be independent, find the standard deviation of the daily revenue.
Questions & Answers
(1 Reviews)
QUESTION:
A gas station earns $2.60 in revenue for each gallon of regular gas it sells, $2.75 for each gallon of midgrade gas, and $2.90 for each gallon of premium gas. Let \(X_1\), \(X_2\), and \(X_3\) denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that \(X_1\), \(X_2\), and \(X_3\) have means \(\mu_1=1500\), \(\mu_2=500\), and \(\mu_3=300\), and standard deviations \(\sigma_1=180\), \(\sigma_2=90\), and \(\sigma_3=40\), respectively.
a. Find the mean daily revenue.
b. Assuming \(X_1\), \(X_2\), and \(X_3\) to be independent, find the standard deviation of the daily revenue.
ANSWER:Step 1 of 3
We have random variables they are:
\(X_{1}\): The number of gallons of regular gas sold in a day.
\(X_{2}\): The number of gallons of midgrade gas sold in a day.
\(X_{3}\): The number of gallons of premium gasoline sold in a day.
Revenue for each gallon of regular gas = $2.60
Revenue for each gallon of midgrade gas = $2.75
Revenue for each gallon of premium gasoline = $2.90
Let us assume that \(X_{1}\), \(X_{2}\) and \(X_{3}\) have means and standard deviations are:
\(\mu_{1}=1500\), \(\mu_{2}=500\), and \(\mu_{3}=300\)
\(\sigma_{1}=180\), \(\sigma_{2}=90\) and \(\sigma_{3}=40\)
Here our goal is:
a). We need to find the mean daily revenue.
b). We need to find the standard deviation of the daily revenue by assuming \(X_{1}\), \(X_{2}\) and \(X_{3}\) to be independent.
Reviews
Review this written solution for 18928) viewed: 1755 isbn: 9780073401331 | Statistics For Engineers And Scientists - 4 Edition - Chapter 2.5 - Problem 10e
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students