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a) Determine the chance of the control manager stopping the lathe when it is operating as designed.

b) Suppose that the machine wears out so that it makes with a mean diameter of 2.04 cm. Determine the probability that the lathe will be allowed to continue.

c) An adjustment error caused the lathe to produce items with a mean diameter of 2.01 cm. Determine the probability that the lathe will be stopped.