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For each question, (a) identify the name of the distribution and justify your choice; (b) define the random variable X in the context of the question; (c) write "what are you trying to fi nd?" in terms of the random variable X (e.g.,P(X=2),E(X), etc); (d) compute the value of the quantity you are trying to fi nd. NOTE that use can use R as a calculator to help you compute some of these probabilities, when the numbers may be too big/small to be properly handled by your calculator. The R command: choose (a, b) computes You will need to use R for most of these questions. 1. 70% of Acadia students prefer Macs to PCs. A random sample of 25 students are interviewed, what is the probability that exactly 20 students prefer Macs? [Hint: use R to compute the probability by changing the following command replacing a, b, and P to numbers from this problem: choose (a,b)pb 2. I have to write a test consisting of 20 multiple choice questions. Each question has 4 options. Having spent the night watching The Big Bang Theory and not studying for this test, I randomly guess at each question. Assuming each question is independent, what is the grade I would expect to get on this test? 3. A sample of 145 Stormtroopers is known to contain 17 individuals with faulty commlinks. If 4 of these Stormtroopers were randomly selected to guard the Millenium Falcon in the Death Star docking bay, nd the probability that two of them have bad commlinks. 4. A restaurant knows from past experience that twelve percent of all reservations do not show. Thirty reservations are expected tonight. What is the probability that 28 reservations do show on this particular night. 5. In Gaspereau Lake, 10 salmon were caught, tagged and released. Later in a second sampling, 12 salmon were caught, and in that sample, 4 salmon had tags. Assuming there are 40 salmon in the lake, calculate the probability that the second sample would contain exactly 4 tagged salmon. 6. A retailer buys most of its test tubes from one speci c manufacturer. The probabil- ity that any one unit produced by this manufacturer is returned to the retailer by a customer due to the fact that the unit does not work properly (i.e., it is defective) is determined to be 0.08. If six test tubes made by the manufacturer are randomly selected and tested, determine the probability that 2 or more are defective. 7. Suppose a box contains 6 red balls and 4 black balls. A random sample of 5 balls is selected. What is the probability of getting exactly 2 red balls if the balls are drawn (i) one at a time with replacement (ii) simultaneously without replacement

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