Question: A manufacturing company produces parts, 97% of which are within specifi- cations and 3% are defective (outside specifications). There is apparently no pattern to the production of defective parts; thus, we assume that whether or not a part is defective is independent of other parts.
(a) What is the probability that there will be no defective parts in a box of 5?
(b) What is the probability that there will be exactly 2 defective parts in a box of 5?
(c) What is the probability that there will be 2 or more defective parts in a box of 5?
(d) Use the Poisson distribution to approximate the probability that there will be 4 or more defective parts in a box of 40.
(e) Use the normal distribution to approximate the probability that there will be 20 or more defective parts in a box of 400.