The quality control manager shuts down an automatic lathe for corrective maintenance whenever a sample of the manufactured items has an average diameter outside the interval (2.01, 2.03) where these figures are in centimeters. The lathe is designed to produce items whose diameters are normally distributed with mean 2.02 cm and standard deviation 0.005 cm.

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.