# 1998%20spring%20answers - Math 218 Final Exam Spring 1998 I...

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Math 218 Final Exam Spring 1998 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. 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) A company with 1,000 employees has the following distribution of salaries for three age groups: under 30 years between 30 and 50 over 50 years under \$50,000 200 250 100 over \$50,000 50 150 250 (a) Find the probability that a randomly chosen employee is at least 30 years old. (b) Find the probability that a randomly chosen employee is under 30 given the employee’s salary is over \$50,000. (c) Find the probability that a randomly chosen employee earns over \$50,000 given the employee is under 30. (d) Determine whether the events that a randomly chosen employee is “aged under 30” and “earns over \$50,000” are independent. Remember to jus- tify your answer. Problem 2 . (20 points) In a certain country 3 out of every 50 inhabitants are infected with malaria. A test is used to detect malaria; however the test is not always accurate. For people without the disease the test gives a false result 1% of the time. For people with the disease the test gives a false result 2% of the time. (a) Draw the probability tree. (b) Find the probability that a randomly selected inhabitant of the country is not infected. (c) Find the probability that a randomly selected inhabitant of the country tests positive (i.e. the test indicates that the person has the disease.) (d) Find the probability that a randomly selected inhabitant of the country who tested positive is infected. Problem 3 . (20 points) A furniture retailer receives a shipment of sixteen so- fas from a factory. Because inspection of each individual sofa is expensive and time-consuming, the retailer has the policy of inspecting a random sam- ple of six items from the shipment. The retailer will accept delivery of the shipment if at most one sampled sofa in the shipment is defective.

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