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Stat 100 Final Exam Spring 2007 Lach problem is worth 20 points. Do one problem ‘Per answer sheet, you may use the back if necessary. All work must be shown to receive full credit. Calculators allowed. 1. In a county, men constitute 60% of the labor force. The rates of. unemployment are 5% for men and 4% for women. Suppose one person is selected at random from the labor force and define the events A = the person is a man, B = the person is unemployed. a) Draw a Venn diagram that depicts this problem. b) What is the probability that the person selected is unemployed? c) What is the probability that the selected person is an unemployed woman? 4) Given that the selected person is unemployed, what is the probability that the person is a man? e) Are the events A and B independent? Justify your answer mathematically. 2. In the finals of the men’s singles tennis championships at Wimbledon, the winner will teceive 655,000 pounds while the runner-up will receive 327,500 pounds. a) Find the expected winnings of a player if the two finalists are evenly matched. b) Find the expected winnings of a player if he has an 80% chance of winning, 3. The proportion of people in the general population with type O blood is .4. Ina group of 14 randomly selected people, find: a) the probability that at most 8 have type O blood b) the probability that at least 6 do not have type O blood c) the expected number with type O blood. d) Use the normal approximation to determine the probability that out of 100 people, at most 50 have type O blood. 4. The weights of apples in a grocery store are normally distributed with mean .32 pounds and standard deviation .08 pounds. a) If one apple is selected at random, what is the probability that its weight will be between .28 and .34 pounds? b) If four apples are selected at random, what is the probability that their average weight will be between .28 and .34 pounds? 5. On the basis of the data of a large sample of speeds of vehicles (mph) on a highway, the 93% confidence interval for the population mean speed is (52.6, 58.2). Use this information to determine: a) a point estimate of 4 and its 95% error margin b) an 80% confidence interval for wv. 6. An insurance company believes that 16% of all claims they handle concern automobile policies. In a random sample of 12,299 claims, 2073 involved automobile policies. a) Test, at level a =.05 , the insurance company’s belief against the alternative that the true proportion is not 16%. Include all of the steps. b) Determine the P-value and comment on the strength of the evidence. 
