A roll of plastic-coated wire has an average of 0.09 flaws per5-meter length of wire. Suppose a quality control engineer willsample a 5-meter length of wire from a roll of wire 230 meters inlength. If no flaws are found in the sample, the engineer willaccept the entire roll of wire.
a. What is the probability that the roll will be rejected?
b. Before examining the sample, what is the probability thatthere are no flaws in the 230 meters of wire? What is theprobability that there are exactly 3 flaws in the entire roll?
c. Based on your answers from parts (a) and (b), what is theprobability that if there is at least one flaw in the entire roll,a randomly sampled 5-meter length of wire from that roll will haveat least one flaw? [Hint: It may be helpful to recognize that ifthe roll has no flaws, the 5-meter length of wire will have noflaws.]
d. Given that no flaws were found in the sample, what is theprobability that the entire roll has no flaws? Is sampling 5 metersof wire sufficient for determining if the entire roll has flaws?Why or why not?
