A gas station earns $2.5 in revenue for each gallon of regular gas it sells, $2.45 for each gallon of midgrade gas, and $2.5 for each gallon of premium gas. Let X1 , X2 , and X3 denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that X1 , X2 , and X3 have means μ1 = 1500, μ2 = 500, and μ3 = 300, and standard deviations σ1 = 180, σ2 = 90, and σ3 = 40, respectively.

a)

And the expected value for R is given by:

b) We have that since are independent

First we need to find the Variance like this:

And replacing we have this:

And using properties of variance w ehave this:

And the deviation would be:

Step-by-step explanation:

We have the following info:

Assuming the following questions:

a) Find the mean daily revenue

Based on the info given the daily revenue is given by:

And the expected value for R is given by:

b) Assuming that X1, X2 and X3 to be independent find the standard deviation for the daily revenue

We have that since are independent

First we need to find the Variance like this:

And replacing we have this:

And using properties of variance w ehave this:

And the deviation would be:

it would be:

c.parallelogram.

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step-by-step explanation: