MSci609_Discussion_Problems

MSci609_Discussion_Problems - Department of Management...

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Unformatted text preview: Department of Management Sciences Faculty of Engineering University of Waterloo MSci 609 Quantitative data Analysis for Management Sciences DISCUSSION PROBLEMS Example 1: Suppose you’re on a game show, and you’re given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door – say, #1 – and the host, who knows what’s behind the doors, opens another door – say #3 – which has a goat. He then says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice? Example 2: A lumber company must decide whether to buy a piece of land containing 5,000 pine trees. If 1,000 of the trees are at least 40 feet tall, the company will purchase the land, otherwise, it will not. The owner of the land reports that the height of trees has a mean of 30 feet and a standard deviation of 3 feet. On the basis of this information, what would be your recommendation to the company? Please explain. Example 3: Six numbers are randomly chosen from 1 to 49 and if you match all six numbers you win the jackpot. Let’s say you are a regular Lotto 6‐49 player and that you buy one ticket. What is the chance that you win the jackpot? Example 4: In answering a question on a multiple‐choice test a student either knows the answer or guesses it. Let p be the probability that she knows the answer, and 1‐p the probability that she guesses. Assume that a student who guesses the answer will be correct with probability 1/m, where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer to a question given that she answered it correctly? Example 5: Family has two children, one of which is a girl. What are the chances the other child is a girl as well? Example 6: A manufacturing operation utilizes two production lines to assemble electronic fuses. Both lines produce fuses at the same rate and generally produce 2.5% defective fuses. However, production line 1 recently suffered mechanical difficulty and produced 6.0% defectives during a three week period. This situation was not known until several lots of electric fuses produced in this period were shipped to customers. If one of the two fuses tested by a customer was found to be defective, what is the probability that the lot from which it came was produced on malfunctioning line 1? (Assume all fuses in a lot were produced at the same line.) ...
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