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Unformatted text preview: 36-225 Handout for Lecture # 23
October 18, 2010 1. Suppose scores on the verbal or math portion of the SAT from a particular year are approximately normally distributed with mean = 500 and standard deviation = 100. What is the proportion of students who scored above 650 that year (or: what is the probability that a randomly chosen student from those taking the exam that year scored above 650?) 2. A life insurance company is interested in the number of claims that it will receive on a particular block of life insurance policies in the coming year. All the policies in the block are written on lives of people who are currently age 79. There are presently 1000 active policies in the block. (None of the policies in the block are written on more than one life, and no insured person is covered by more than one policy.). Based on the United States Life Tables, the company estimates that the probability of any given 79-year-old dying in the next year is .05. Assume that the future lifetime of the insured persons are independent. Determine the probability that the company receives no more than 60 claims on this block of 1000 policies in the coming year. 3. The life length of a certain electronic device varies exponentially with = 40 hours. (a) What is the probability that the device works more than 45 hours? (b) If the device has been working for 40 hours, what is the probability that it continues working at least an additional 10 hours? ...
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