MATH 218 Fall97final

MATH 218 Fall97final - Math 218 Final Exam Fall 1997...

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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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This note was uploaded on 02/13/2009 for the course MATH 218 taught by Professor Haskell during the Spring '06 term at USC.

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MATH 218 Fall97final - Math 218 Final Exam Fall 1997...

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