Question: A shipment of 100 pins contains some defectives. To decide whether to accept the shipment, the consumer follows a sampling plan where 15 items are chosen at random from the sample and tested. If the number of defectives in the sample is at most one, the shipment is accepted. (The number 1 is known as the acceptance number of the sampling plan.)

a. Assuming that the shipment includes 5% defectives, what is the probability that the shipment will be accepted? (Hint: Use the hypergeometric distribution.)

b. Assuming that the shipment includes 8% defectives, what is the probability that the shipment will be accepted?

c. Using the Data Table command, tabulate the probability of acceptance for defective percentage ranging from 0% to 15% in steps of 1%.

d. Plot a line graph of the table created in part (c) above. (This graph is known as the operating characteristic curve of the sampling plan.)