A simple cylinder is machined by separate turning and cutting operations, each producing independent and normal distributions of outside diameter and length dimensions. Assume the resulting volume of the cylinder is also normally distributed. The volume has upper and lower specification limits of 1.7662 and 1.6516 in^3 respectively. The volume must have a minimum Cpk of 1.33 before the turning and cutting operations can be released for production. The turning operation produces a mean diameter of 1.015 in and a standard deviation of 0.004 in.(a) Determine the mean length necessary from the cutting operation to 'center' the volume within its specification limits.(b) Assume that the centering of part (a) can be accomplished and maintained. Determine the largest allowable standard deviation of the length dimension from the cutting operation.