Apple Products Inc., an apple products firm and its apple fruit suppliers have agreed to an incoming inspection procedure called "Accepting sampling". When a truck load of apples arrives at firm's packaging plant, for a lot size of 1000 apples, a random of 40 apples is selected for bruises, discoloration, and other defects. The whole truckload of apples will be rejected if more than 3 of the apples are defective. Otherwise the whole truck load is accepted.

a) Suppose a truck arrives with a population defective rate 3% (i.e., 3% of the apples do not meet the acceptance standard). What is the probability that this truck will be rejected?

b) Please calculate the average outgoing quality at this point.

c) Please calculate the average total inspection value at this point.

d) Suppose that Apple Products Inc. firm and its apple fruit suppliers have agreed on the following sampling plan: ?=5%, ?=10%, AQL=1% and LTPD=5%. Select a sampling plan that exactly meets the supplier's stipulation and comes as close as possible to the Apple Products Inc. firm's stipulation.