8. (10 points) {i} Exercise 4.49 in SEE 011 page 111. [ii] Exercise 4.52 in SEE e11 page 177. {iii} Exereise 4.71] in SEE 011 page 130. 4.49 Which of these acceptance rules has the smaller probability of accepting a shipment containing 20% detectives? A company receives large shipmenls of parts from two sources. Seventy percent of the shipments come from a supplier whose shipments typically contain 10% defectives, while the remainder are from a supplier whose shipments typically contain 20% defectives. A manager receives a shipment but does not know the source. A random sample of 20 items from this ship- ment is tested, and 1 of the parls is found to be defec- tive. What is the probability that this shipment came from the more reliable supplier? (Hint: Use Bayes' theorem.) 4.62 A new warehouse is being designed and a deci- sion concerning the number of loading docks is required. There are two models based on truck- arrival assumptions for the use of this warehouse, given that loading a truck requires 1 hour. Using the first model, we assume that the warehouse could be serviced by one of the many thousands of inde- pendent truckers who arrive randomly to obtain a load for delivery. It is known that, on average, 1 of these trucks would arrive each hour. For the second model, assume that the company hires a fleet of If] trucks that are assigned full time to shipments from this warehouse. Under that assumption the trucks would arrive randomly, but the probability of any truck arriving during a given hour is [1.1. lClbtain the appropriate probability distribution for each of these assumptions and compare the results. _, am A bank executive is presented with loan applications from N] people. The profiles of the applicants are similar, except that 5 are minorities and 5 are not mi- norities. In the end the executive app roves 6 of the ap- plications. If these 6 approvals are chosen at random from the 10 applications, what is the probability that fewer than half the approvals will be of applications involving minorities