Suppose you are a production manager for a small firm that manufactures GPUs (i.e., video cards) for computers. Your production facility utilizes three identical machines. Quality is binary — each GPU is either defective or it is not defective. Machine 1 produces 40 GPUs per day, and past experience suggests that, on average, 2% of its output will be defective. Machine 2 produces 20 GPUs per day, and past experience suggests that, on average, 3% of its output will be defective. Machine 3 produces 10 GPUs per day, and past experience suggests that 4% of its output will be defective. Any unit of output is not identifiable as having been produced by Machine 1, 2 or 3. (a) Suppose that on March 3, 2022, one GPU is randomly selected from the day’s 70 units of production. That unit is found to be defective. What is the probability that that defective unit was produced by Machine 1? Machine 2? Machine 3?
Suppose you are a production manager for a small firm that manufactures GPUs (i.e., video cards) for computers. Your production facility utilizes three identical machines. Quality is binary — each GPU is either defective or it is not defective. Machine 1 produces 40 GPUs per day, and past experience suggests that, on average, 2% of its output will be defective. Machine 2 produces 20 GPUs per day, and past experience suggests that, on average, 3% of its output will be defective. Machine 3 produces 10 GPUs per day, and past experience suggests that 4% of its output will be defective. Any unit of output is not identifiable as having been produced by Machine 1, 2 or 3.
(a) Suppose that on March 3, 2022, one GPU is randomly selected from the day’s 70 units of production. That unit is found to be defective. What is the probability that that defective unit was produced by Machine 1? Machine 2? Machine 3?
(b) Now suppose that on March 4, 2022, the firm operates only Machine 1. Of its 40 units of output, 4 were found to be defective. This could happen by chance. But if the firm assesses the probability of this happening to be less than 5%, it has a policy to have the Machine serviced. What should the firm do?
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