A machine produces parts continuously throughout the day with an overall defect rate of 0.80%. Periodically a random sample of 50 parts is sampled, and if 3 or more are found to be defective the machine is stopped and adjusted.

a. What is the probability that in the next sample of 50 parts the machine is stopped for adjustment?

b. What is the probability that in the next sample of 50 parts the machine is allowed to keep processing parts even though its defect rate has increased to 1.1%?

c. How many parts would need to be sampled, on average, in order to find one defective part if the overall defect rate is 0.80%?