2001%20fall - Fall 2001 Math 218 common final exam R Bruck...

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Fall 2001 Math 218 common final exam R. Bruck, L. Goukasian, C. Haskell, I. Kukavica, F. Lin, J. Novak, L. Piterbarg, G. Rosen, H. von Bremen Problem 1 (20 points) . In a MATH 218 class there are a total of 50 students. There are 30 female students, 9 of whom do not own a car. Among the male students 6 do not own a car. (a) Use either a contingency table or a tree, to organize the data. (b) Find the probability that a randomly selected student owns a car and is female. (c) Find the probability that a randomly selected student is female, given that the student owns a car. (d) Are the events “is female” and “owns a car” independent? Explain. Problem 2 (15 points) . The probability of at least one Category 5 (C5) hurricane occurring in the Pacific Ocean during any given year is 10%. Scientists at the Ocean Institute have been predicting whether or not a C5 hurricane would occur in each calendar year with mixed results. In years when C5 hurricanes have occurred, their predictions have been correct 60% of the time. In years when no C5 hurricane occurred they have been correct 80% of the time. a) The Ocean Institute is predicting that a C5 hurricane will occur in 2002. Find the probability that such an event will occur given their previous record. b) Scientists at the rival Atmospheric Sciences Service predict a C5 event in 2003 and have predicted such an event every year. Find the probability of a C5 event based on the Atmospheric Sciences Service’s record. Problem 3 (20 points) . The Giant Miniatures Company is implementing the Ultimate Quality Review (UQR) staff development program by randomly choosing managers for training. Among all the managers in the company, 35% have already completed the older Total Program Improvement (TPI) training program. a) If an initial group of 10 managers is chosen at random from the company, find the probability that at least 2 of them will have completed the TPI training. b) A total of 120 managers from Giant Miniatures will be trained in the UQR program. Approximate the probability that between 30 and 40, inclusive, of these randomly selected managers will be graduates of the TPI program.
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