Question 1:

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, 1% 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. On April 7, 2021, post-production quality inspection of the day's output of 70 GPUs revealed that 6 were defective. This could happen by chance. But if the firm assesses the probability of this happening to be 5% or less, its policy is to have one or more of its machines serviced. What should the firm do?