1997%20fall%20answers - Math 218 Final Exam Fall 1997...

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Math 218 Final Exam Fall 1997 Instructions. Every numerical answer should be simplified to a frac- tion or decimal. You must show your work and justify your methods to obtain full credit. Use the continuity correction wherever it is appropri- ate 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 cus- tomers asked them to rate their brokers. The results have been tab- ulated 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 probability 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 independent. 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.
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