Gerald Black of BlackFly Airline has an exclusive contract to run flights of a four-passenger aircraft to a remote mining center.His contract requires him to fly if there are any passengers wanting to make the trip. His fixed costs per day are $300,his fixed costs per flight are $1,300.00, the variable cost per passenger is $20.00, and he charges $800.00 per passenger.

He has tracked the number of passengers who flew with him over the past sixty days. His findings are summarized in the following table:

Number of Passengers

0

1

2

3

4

Number of Days

3

10

17

20

10

For example, on 17 of the 60 days during tracking, there were 2 passengers.Note that on the 3 days when there were no passengers Gerald does not fly but still incurs his daily fixed costs (primarily rent).

Assume that this sample gives a good approximation to his future demand patterns.Let G be the random variable: profit on a future day.

a)Calculate the Expected Value, E[ G ], Variance, s²[ G ]and standard deviation, s[ G ], of his future daily profit.[Hint: You can calculate a profit corresponding to each number of passengers.The probabilities of those profits are then determined by the probabilities of the numbers of passengers.]

b)Comment briefly on the profitability and volatility of Gerald's business.