Extra Questions 1. Suppose that the probability is 0.1 that the value of the Jamaican dollar will rise against the U.S. dollar over any given week and that the outcome in one week is independent of that in any other week. What is the probability that the value of the Jamaican dollar will rise against the U.S. dollar at least twice over a period of 7 weeks? ECON1005: INTRODUCTORY STATISTICS PROBLEM SET 6 2. Suppose you take a multiple-choice test which covers particle physics (something none of us know anything about). The test consists of 40 questions, each having 5 options. If you guess at all 40 questions, what are the mean and standard deviation of the number of correct answers? 3. 4. The following two acceptance rules are being considered for determining whether to take delivery of a large shipment of components: A random sample of 10 components is checked, and the shipment is accepted only if none of them is defective. A random sample of 20 components is checked, and the shipment is accepted only if no more than 1 of them is defective. Which of these acceptance rules has the smaller probability of accepting a shipment containing 20% defectives? You must justify your answer with clear calculations. A bond analyst was given a list of twelve corporate bonds. From that list, she selected three whose ratings she felt were in danger of being downgraded in the next year. In actuality, a total of four of the twelve bonds on the list had their ratings downgraded in the next year. Suppose that the analyst had simply chosen three bonds randomly from this list. What is the probability that at least two of the chosen bonds would be among those whose ratings were to be downgraded in the next year? Assume that the probability of one bond being downgraded is independent of another.