You are a quality control engineer and you are in charge of certifying that a batch of resistors is ok for inclusion in products. The batch has 100 resistors. Your company policy is that the batch is good and you should accept it as long as 90% of the parts are good. Sampling all 100 is time consuming, so you sample 10. Your rule is that if there are 2 or more bad ones in the10 you reject the entire batch. If there are one or zero bad ones, then you accept the entire batch.
a. Assume that the sample has 90 good and 10 bad. What is the probability that you will actually accept the batch? That is, what is the probability that your draw will have 0 or 1 bad resistors?
b. Assume that the sample has 95 good and 5 bad (so it is a good batch). What is the probability that you will reject the batch? That is, what is the probability that you will draw 2 or more bad resistors? Hint: this may be easier to do with subtraction.
c. The answers in a. and b. are really the probabilities that you will make errors. Rejecting good batches and accepting bad batches are errors. How could you change your sampling plan to reduce these errors? Discuss and give examples.