Single-sample acceptance sampling for attributes uses a procedure similar to that of Exercise 19, Suppose that a sampling plan for accepting a lot of size N coming to a manufacturer from a supplier is to be determined by sampling n items from the lot and accepting the entire lot if e of fewer of the items are defective. The lot fraction defective, p, is the true proportion of defective items in the lot. The probability of observing or defective items in a random sample of nitems can be calculated using the binomial distribution. The probability of observing e or fewer defective items is the sum of the probabilities from 0 to c and is called the probability of acceptance, P. An operating characteristic (OC) curve is then constructed plotting P versus p. This OC curve illustrates the performance of a sampling plan using n items and an acceptance value of c. Construct an OC curve for the sampling plan n = 50 and c = 1. 19. During 1989, a certain trucking company purchased 500 tires from a local dealer. The dealer guaranteed the tires to withstand loads of up to 100,000 pounds at speeds up to 55 mph. The drivers for the trucking company complained that the tires were not living up to this guarantee and were failing the first trip they were used. The trucking company decided to sample the tires and send them to an engineering firm for testing. This testing is expensive and destructive; therefore, the sample size to be tested must be carefully chosen. Construct a sampling plan for the company by doing the following: (a) Calculate the probability of getting all defective tires in samples of size 25,30, and 50 for p = 0.80, 0.90, 0.95, and 0.99, where p is the probability that an individual tire will fail. (Use the binomial distribution.) (b) Graph these probabilities against p for the various values of n on the same graph. Use this graph to suggest a sample size.