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# 260hw2 - MATH 260 HOMEWORK 2(Due March 8 2011...

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February 28, 2011 MATH 260 HOMEWORK # 2 (Due March 8, 2011, Tuesday) (Please submit your solutions to my office by 5:00 p.m, latest) 1. A machine in a heavy-equipment factory produces steel rods of length Y, where Y is a normally distributed random variable with μ = 6 inches and σ 2 = 0.2. The cost C (in dollars) of repairing a rod that is not exactly 6 inches in length is C = 4( Y – μ ) 2 . If 50 rods with independent lengths are produced in a given day, approximate the probability that total cost for repairs exceeds 48 dollars. (Note that ) ( ~ 2 1 2 n Z n i i χ = . Since ) ( 2 n is actually sum of random variables by C.L.T, for large n, ) ( 2 n is approximately normally distributed. Use this fact to solve the problem.) 2. Civil engineers believe that W, the amount of weight (in units of 1000 pounds) that a certain span of a bridge can withstand without structural damage resulting, is normally distributed with mean 400 and standard deviation 40. Suppose that weight (again, in units of 1000 pounds) of a car is a random variable with mean 3

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260hw2 - MATH 260 HOMEWORK 2(Due March 8 2011...

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