Problem 2: A manufacturing line makes parts that have a defect rate of 1 in 100; that is, one part out of every 100 parts on average are bad, and the remaining parts are good. (a) You have an original testing system that is 95% accurate in determining whether a part is defective or works, and its accuracy is the same for both good parts and bad parts. Suppose your original testing system labels a particular part defective. What is the probability that the part is bad? (5 points) (b) You decide to obtain a second improved testing system that can tell if a good part works with 99% accuracy, but it can only tell if a bad part is defective with 95% wecuracy like the original testing system. You decide to use the second improved testing system to screen only the parts that are labelled defective by the original testing system, where a part is declared overall defective only if the two-stage testing process labels it defective. In this two-stage testing setup. for each part determined overall defective, what is the probability that the part is bad? (10 points) (c) Testing parts on a manufacturing line is a complex design process in- volving a number of requirements and constraints. Based on the results of (a) [Method A) and (b) Method B) in this problem, answer the fol lowing questions, and provide brief comments on the final prompt below: (1) Functionality: Which testing process produces a more accurate as- sessment of a part's defectiveness. Method A or Method B? (2) Maintainability: Which testing process requires less effort and ex- pense to maintain, Method A or Method B? (3) Sustainability: Which testing process results in less waste being produced by the manufacturing plant, Method A or Method B? (4) Schedule: Which testing process takes less time and keeps the man- ufacturing line moving the fastest, Method A or Method B? (Comment) Given these answers, briefly comment on how these and other parameters of the testing process might impact the overall cost of parts produced on a manufacturing line, which affects the economics of manufacturing in general (10 points)