HM2 - China MIM PDF

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China MIM...

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Homework for QM Lecture 2 (Discrete Probability Distributions) 1. The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2. a. Show the probability distribution for the expense forecast. b. What is the expected value of the expense forecast for the coming year? c. What is the variance of the expense forecast for the coming year? d. If income projections for the year are estimated at $12 million, comment on the financial position of the college. 2. A company is planning to interview Internet users to learn how its proposed Web site will be received by different age groups. According to the Census Bureau, 40% individuals aged 18-54, and 12% of individuals aged 55 and older use Internet. a. How many people from the 18-54 age group must be contacted to find an expected number of at least 10 Internet users? b. How many people from the age groups 55 and older must be contacted to find an expected number of at least 10 Internet users? c. If you contact the number of 18- to 54-year-old people suggested in part (a), what is the standard deviation of the number who will be Internet users? d. If you contact the number of people age 55 and older suggested in part (b), what is the standard deviation of the number who will be Internet users? 3. Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour. What is the probability that 20 or more cars will arrive during any given hour of operation?...