Math 218
Final Exam
Fall 1997
I
NSTRUCTIONS
. Every numerical answer should be simplified to a fraction
or decimal. You must show your work and justify your methods to obtain
full credit. Use the continuity correction wherever it is appropriate unless
otherwise instructed. If you can’t do one part of a problem but need that
answer later, guess an answer and use that guess for the later part. The exam
is worth a total of 200 points.
Problem
1
.
(20 points) The manager of a brokerage firm with 500 customers
asked them to rate their brokers. The results have been tabulated below. The
columns describe the customers’ incomes and the rows describe their ratings
of the brokers.
Under $20,000
$20,000 to $50,000
Over $50,000
Excellent
50
60
40
Average
100
120
50
Poor
30
35
15
(a) Find the probability that a randomly selected customer has an income
between $20,000 and $50,000.
(b) Given that the customer has an income below $20,000, find the proba
bility that the customer gave the broker an average rating.
(c) Given that the customer has an income of $20,000 or above, find the
probability that the customer gave the broker an average rating.
(d) Determine whether the events ‘excellent’ and ‘over $50,000’ are inde
pendent.
Problem
2
.
(25 points) An oil company is about to drill at a particular site.
The rock layers at the site may or may not have a ‘dome structure’. A dome
structure increases the chance of finding oil.
The probability that there is a dome structure at the site is 0.6. If there is a
dome structure the probability that the site is dry is 0.6, the probability that the
site is a low producer is 0.3 and the probability that the site is a high producer
is 0.1. If there is no dome structure the probability that the site is dry is 0.8,
the probability that the site is a low producer is 0.15 and the probability that
the site is a high producer is 0.05.
If the site is dry the payoff will be
−
$100,000 (loss of $100,000); if it is a low
producer the payoff will be $200,000; if it is a high producer the payoff will
be $500,000.
(a) Draw the probability tree.
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 Spring '06
 Haskell
 Math, Continuity, Normal Distribution, Probability, Statistical hypothesis testing, producer

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