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Unformatted text preview: 3.9 Exercises 141 pate in class. However, before she goes to bed, she must start and then complete a homework assignment which is due tomorrow morning. According to her experi ence, the time it takes her to complete a homework assignment for this class is Nor mally distributed with mean 11 = 3.5 hours and standard deviation (T = 1.2 hours. Helen looks at her watch and sees that it is now 6:00P.M.What is the probability that she will be able to get to bed in time to be sufficientlyrested for the next day's class? EXERCISE 3.6Winter lasts from December 21 through March 21. The average win ter temperature in Boston is Normally distributed with mean 11 = 32.5 F and stan dard deviation (T = 1.590F. In New York City, the average winter temperature is Normally distributed with mean 11 = 35.4 F and standard deviation (T = 2.05 F. (a) What is the probability that the average winter temperature in Boston this com ing winter will be above freezing (32 F)? (b) Assume that average winter temperatures in Boston and New York are inde pendent. What is the probability that the average temperature in Boston in the coming winter will be higher than in New York? (c) Do you think the independence assumption above is reasonable? EXERCISE 3.7 In a large shipment of tomatoes, the weight of each tomato is Nor mally distributed with mean 11 = 4.2 ounces and standard deviation (T = 1.0 ounce. Tomatoes from this shipment are sold in packages of three. (a) Assuming the weight of each tomato is independent of the weights of other toma toes, compute the mean and the standard deviation of the weight of a package. (b) Compute the probability that a package weighs between 11.0 and 13.0 ounces. EXERCISE 3.8 MIT's pension plan has two funds, the fixed income fund and the variable income fund. Let X denote the annual return of the fixed income fund. Let Y denote the annual return of the variable income fund. We assume that X obeys a Normal distribution with mean 7% and standard deviation 2%, and that Y obeys a Normal distribution with mean 13%and standard deviation 8%. We also assume that CORR (X, Y) = 0.4. A particular 0....
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 Spring '07
 JosephGeunes
 Normal Distribution, Standard Deviation, Probability theory, S&P 500 Index, Dow Jones Index

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