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 X1, X2, X3 denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day.
Assume that X1, X2, X3 have means μ1 = 1500, μ2 = 500, and μ3 = 300, and standard deviations σ1 = 180, σ2 = 90, and σ3 = 40, respectively.
a. Find the mean daily revenue.
b. Assuming X1, X2, and X3 to be independant, find the standard deviation of the daily revenue.