We are manufacturing electric toothbrushes. Realizing that nothing is perfect, we do have a defective rate (meaning anything at all wrong with the product) of 4%.

(a) If we have a batch of 100 toothbrushes, how many do we expect to be defective?
(b) We select 2 toothbrushes from our batch of 100 - what is the proper sampling technique?
(c) Find the probability that out of our batch of 100, with the sampling technique listed above, that (i) both toothbrushes are defective, (ii) that one of the two is defective.

Now... we have a new production manager who has made many changes. She feels that her defective rate is lower than what occurred before. She manufactures a batch of 10,000 toothbrushes and from this batch selects 200. She finds that there are no defects in the 200 selected.

(a) Assuming that the new method has the same 4% defective rate as we have seen previously, what is the probability that there are no defects in her sample of 200?
(b) Given the preferred sampling technique, how do explain how you can do what you did in part (a)?
(c) Based on your results in part (a), do you feel that there is strong evidence to support our manager's claim that her new process is better?