Question: Fuel Consumption and Cars Companies receiving large shipments of raw materials of any product often use a specific plan for accepting the entire shipment. An acceptance sampling plan usually includes the sample size for close inspection, the acceptance criterion, and the rejection criterion. For a given plan, the operating characteristic (OC) curve shows the probability of accepting the entire lot as a function of the actual quality level. Standard clip-on weights for steel rims on automobiles (used when tires are balanced) are available in (1/4)-ounce to 6-ounce sizes. Suppose an automobile garage receives a large shipment of 2-ounce weights. A garage mechanic will select a random sample of 30 weights and weigh each one on a precise scale. If the sample mean is within 0.05 ounce of the printed weight (of 2 ounces), then the shipment is accepted. Otherwise, the entire shipment is rejected and returned to the manufacturer. Suppose the population standard deviation is 0.13 ounce.
a. Find the probability of accepting the entire shipment if the true population mean weight is 1.86, 1.88, 1.90, 1.92, 1.94, 1.96, 1.98, 2.00, 2.02, 2.04, 2.06, 2.08, 2.10, 2.12, of 2.14 ounces.
b. Plot the probability of accepting the entire shipment versus the true population mean weight. The resulting graph is the OC curve for the given acceptance sampling plan.