Question: The quality control manager shuts down an automatic lathe for corrective maintenance whenever a sample of parts it produces has an average diameter either exceeding

The quality control manager shuts down an automatic lathe for corrective maintenance whenever a sample of parts it produces has an average diameter either exceeding 2.01 inches or smaller than 1.99 inches. The lathe is designed to produce parts with a mean diameter of 2.00 inches and a standard deviation of 0.005 inches. Assuming normality, suppose a part wears out so that it makes parts that are on the average too wide (2.02 inches), what is the probability that the lathe is allowed to continue?

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