7. (a) (5.95) (Hypergeometric- Quality Control A production process produces items in lots of 50. Sampling plans exist in which lots are pulled aside periodically and exposed to a certain type of inspection. It is usually assumed that the proportion of defective in the process is very smal. It is also important to the company that lots containing defects be a rare event. Currently the inspection plan by the company is to periodically sample randomly 10 out of the 50 in a lot and if noe are defective, no intervention into process is done. i. Suppose in a lot chosen at random, 2 out of 50 are defective. What is the proba- bility that at least 1 in the sample of 10 from the lot is defective? i. From your answer in (i), comment about the quality of this sample plan. ii. What is the mean number of defects found out of 10? (b) (5.96) (Increase Sample Size n Quality Control) Refer to part (a), it has been determined that the sampling plan should be extensive enough that there is a high probability, say 0.9, that if as many as 2 defectives exist in the lot of 50 being sampled at least 1 will be found in the sampling. With these restrictions, how many of the 50 items should be sampled (c) (5.99) (Binomial Approximation to Hypergeometric) Go back to part (a)(i). Re-compute the probability using the binomial distribution. Comment