4 (20 Points): (Acceptance Sampling) The AQL and LTPD of a single sampling plan are 0.03 and 0.06, respectively. Your company is more risk-averse than others in purchasing from suppliers and is interested in finding a single sampling plan such that the probability of rejecting a lot with a percentage nonconforming of 0.03 (i.e., the AQL) is 5% and the probability of accepting a lot with a percentage nonconforming of 0.06 (i.e., the LTPD) is 5%. Part (a): (8 Points) Please provide two equations that can be used to determine the two unknowns of the plan (n, c). For each of the two equations, specify the Pa and p. Part (b): (5 Points) What should be the plan? Approximate numbers will suffice. Draw on the nomograph to show your work. (Do not attempt to solve the two equations for the two numbers n and c.) Part (c): (5 Points) When the lot size N is not very large when compared with the sample size n, is the binomial distribution used in the answer of Part (a) justified? If so, explain why. If not, what distribution should be used? Part (d): (2 Points) Returning lots to the vendor is obviously undesirable for the vendor; it may also negatively impact your company. Describe one negative impact in up to two sentences