A gas station eams $2.36 in revenue for each gallon of regular gas that it sells

Question

A gas station eams $2.36 in revenue for each gallon of regular gas that it sells, $2.46 for each gallon of midgrade gas, and $2.66 for each gallon of premium gas. Let X X2, and X3 denote the number of gallons sold for each of these types of gas in a day The mean sales amounts in gallons for the three grades are 1700, 400, and 200. The standard deviation of the daily amount sold by grade is 200, 80, and 35 gallons respectively. Find the mean revenue from the gas and the standard deviation of the revenue, assuming that the amounts sold by grade are independent.

Explanation / Answer

here total revenue R =2.36X1+2.46X2+2.66X3

hence mean revenue E(R)=2.36*E(X1)+2.46*E(X2)+2.66*E(X3)

=2.36*1700+2.46*400+2.66*200=5528

sd deviation revenue SD(R)=sqrt(2.362*Var(X1)+2.462*Var(X2)+2.662*Var(X3))

=sqrt(2.362*2002+2.462*802+2.662*352)=519.79

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