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, 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.

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facundo3141592 facundo3141592 · Answer 1 · 2019-10-13T22:41:23+02:00

Answer: 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