Vendor A supplies parts, each of which has probability 0.03 of being defective. Vendor B also supplies parts, each of which has probability 0.05 of being defective. You receive a shipment of 100 parts from each vendor.
a. Let X be the number of defective parts in the shipment from vendor A and let Y be the number of defective parts in the shipment from vendor B. What are the distributions of X and Y?
b. Generate simulated samples of size 1000 from the distributions of X and Y.
c. Use the samples to estimate the probability that the total number of defective parts is less than 10.
d. Use the samples to estimate the probability that the shipment from vendor A contains more defective parts than the shipment from vendor B.
e. Construct a normal probability plot for the total number of defective parts. Is this quantity approximately normally distributed?