15.Math-Review.ppt

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15.Math-Review.ppt

15.Math-Review Exercises Exercises Exercises Exercises Exercises Exercises Exercises Exercises Solutions Solutions * * Review 2 P1. Historical data indicates that the starting salary for a new MBA graduate in a leading management consulting firm can be modeled as a normal distribution with mean $90,000 and standard deviation $20,000. Second year salaries increase by 20%. The bonus each year, for the first and following years, can be modeled as a normal distribution with mean $25,000 and standard deviation $5,000. We assume that the bonus is independent of the initial salary increase. For the purpose of this problem annual compensation is salary plus bonus. (a) What is the expected annual compensation for a new hire? (b) What is the standard deviation of the annual compensation for a new hire? (c) What is the expected annual compensation after completing a year in the firm, I.e., just after the salary increase is announced? (d) What is the probability that the annual compensation after completing a year in the firm, i.e., just after the salary increase is announced, will exceed $140,000? (Hint: The annual compensation is also normally distributed). P2. Suppose 5% of the microchips produced by a leading microchip manufacturer are defective. An inspector inspects 10 microchips. Historically, given that a microchip is defective, the inspector accepts it 10% of the time thinking it has no defect. If a microchip is not defective, he always correctly accepts it. (a) What is the probability that all 10 microchips in the sample are not defective? (b) What is the probability that the inspector accepts the first microchip? (c) What is the probability that the inspector accepts 9 (out of 10) microchips? (d) Given that the inspector accepts a microchip, what is the probability that it has no defect? P3. To the best of our knowledge, with probability 0.8 Al is guilty of the crime for which he is about to be tried. Bo and Ci, each of whom knows whether or not Al

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