Homework2_Solutions - ISOM 111 L7-L8 Fall 2010 1 Homework 2...

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Unformatted text preview: ISOM 111 L7-L8, Fall 2010 1 Homework 2 Solutions I. At a large assembly line, the manufacturer reassigns employees to different tasks each month. This keeps the workers from getting bored by endlessly repeating the same task. It also lets them see how the work done in different stages must fit together. It is known that 55% of the employees have less than or equal to two years of experience, 32% have between three and five years of experience, and the rest have more than five years of experience. Assume that teams of three employees are formed randomly. Dave works at this assembly line. (a) Consider one of Dave’s teammates. What is the probability that this teammate has (a.1) two or fewer years of experience? (a.2) more than five years of experience? (b) What is the probability that, considering both of Dave’s two teammates, (b.1) both have more than two years of experience? (b.2) exactly one of them has more than five years of experience? (b.3) at least one has more than five years of experience? Ans : (a.1) P (2 or less) = 0 . 55 (a.2) P (more than 5) = 1- (0 . 55 + 0 . 32) = 0 . 13 (b.1) P (more than 2 and more than 2 ) = 0 . 45 2 = 0 . 2025 (b.2) P (exactly one more than 5) = P (more than 5 and not more than 5) + P (not more than 5 and more than 5) =2 × P (more than 5) P (5 or less) = 2 × . 13 × . 87 = 0 . 2262 (b.3) P (at least one with more than 5) = 1- P (both have 5 or less) = 1- . 87 2 = 0 . 2431 which is the answer to the prior question plus the probability that both have more than 5 years of experience (0 . 13 2 = 0 . 0169) II. A product is assembled using 10 different components, each of which must meet specifica- tions for five different quality characteristics. Suppose that there is a .9973 probability that each individual specification will be met. (a) Assuming that all 50 specifications are met independently, find the probability that the product meets all 50 specifications. (b) Suppose that we wish to have a 99.73 percent chance that all 50 specifications will be met. If each specification will have the same chance of being met, how large must we make the probability of meeting each individual specification? ISOM 111 L7-L8, Fall 2010 2 Ans : a. By independence, the probability is 0 . 9973 50 = 0 . 874....
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Homework2_Solutions - ISOM 111 L7-L8 Fall 2010 1 Homework 2...

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