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
