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(ISMT111)Mid04.pdf
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ISMT111 Business Statistics
Midterm Examination

For sections 3, 4, 5 & 6 only

15th October 2004
Directions
1) Answer ALL FIVE questions. Marks are shown in square brackets.
2) There are 4 pages in this examination paper. Check to make sure you have a complete set and notify the invigilator immediately if part of it is
missing.
3) Key formulas and Statistical tables are provided separately.
4) Calculator may be used in this examination.
5) You are given TWO HOURS to complete this examination. Do not
begin until you are told to do so.
Question 1: [22 Marks]
Airlines often intentionally overbook flights knowing that not everyone who purchased a ticket for the flight will actually show up. Suppose that there is a 98% chance that a passenger with a ticket will actually show up for the flight. Consider a particular flight has 85 seats and the airline sold 88 tickets for the flight.
(a)
What assumption is needed in order to claim that the number of passengers showing up is a binomial random variable? Hereafter, you can answer the following parts with such an assumption.

(b)
What is the expected number of passengers that will show up?

(c)
Suppose that all tickets are purchased for $375. If more passengers show up than there are seats available for the flight the airline will have to pay $1000 to each passenger without a seat. Assume that the airline keeps the money from tickets purchased even if the passenger doesn't get on the flight. (Hint: Do NOT use normal approximation in part (c).)

(i)
What is the probability that the airline will not need to pay any money to the passengers for overbooking?

(ii)
What is the distribution of the airline net revenue (Hint: Net revenue=revenue




minus the payout for overbooking)? (iii)What is the airline expected net revenue? (iv)Give a reason why normal approximation may give a significant error for the
computations of the airline net revenue.

Question 2: [22 Marks]
You have mineral rights on a piece of land that has a probability of 0.1 of containing oil. If you test drill and it does contain oil, the payoff is $200,000,000. However, it costs $10,000,000 to perform the drilling.
Before test drill you can consult a geologist who can assess the promise of the land. She can tell whether your prospects are good or not good, but she is not a perfect predictor. If there is oil, the conditional probability that she will say that the prospects are good is 0.9. If there is no oil, the conditional probability that she will say that prospects are not good is 0.85. The geologist charges $700,000 as her consulting fee.
(a)
Suppose you consult the geologist and she says that the prospects are good.

(i)
What is the probability that you will strike oil if you test drill?

(ii)
What is the expected profit if you test drill?



(b)
Suppose you consult the geologist and she says that the prospects are not good.

(i)