Agas 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, 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=550, μ3=300, and standard deviations, σ1=180, σ2=100, σ3=35, respectively. a. find the mean daily revenue.
b. assuming x1, x2, and x3 to be independent, nd the standard deviation of the daily revenue.

Hello there!

for regular gas the gas station earns $2.60 per gallons, the mean number of gallons sold is x1 = 1500 with a standard deviation of 180.

then the mean revenue for this regular gas is: $2.60*1500 = $3900

and the deviation is $2.60*180 = $468

for midgrade gas the gas station earns $2.75 per gallons, the mean number of gallons sold is x1 = 550 with a standard deviation of 100.

Then the mean revenue for this gas is: $2.75*550 = $1512.5

the standard deviation is: $2.75*100 = $275

for premiun gas the gas station earns $2.90 per gallons, the mean number of gallons sold is x1 = 300 with a standard deviation of 35.

The mean revenue is: $2.90*300 = $870

with a standard deviation of : $2.90*35 = $101.5

a) Then the mean daily revenue for the gas station is the sum of the mean revenue for each type of gas:

$870 + $1512.5 + $3900 = $6282.5

b) because the events are independent, we also should add the standard deviations; this is:

$468 + $101.5 + $275 = $844.5

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