A quality control inspector accepts shipments of 500 precision ½" steel rods if the mean diameter of a sample of n = 100 falls between 0.4995" and 0.5005". Previous evaluations have established that the standard deviation for individual rod diameters is 0.003".

a. Determine the probability that the inspector will accept an almost out-of-tolerance shipment that actually has H 0.5003 cm.

b. Determine the probability that the inspector will (mistakenly) reject a near-perfect shipment that actually has u = 0.4999 cm.