Consider the diameters of cylindrical parts manufactured on a computer-controlled lathe. a) Suppose that the mean of the diameters is known to be 0.1 millimetres. Give an upper bound to the probability that the diameter of new part will exceed 0.11 mm. b) Suppose that the mean is unknown but the standard deviation is known to equal 0.002 mm. What can be said about the probability that the diameter of a new part will be within 0.006 mm of the unknown mean for that run? c) How many new parts should be made so as to ensure, with probability at least 0.75, that the average diameter would be within 0.001 mm of the unknown mean? Assume each part is made independently.