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 pis 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.