Question: Problem #3: A cable manufacturer has historically averaged 2.6 flaws per 1000 meters length of wire production.

(a) Find the probability that has one or fewer flaws.

(b) Find the probability that a 1000 length of wire has more than one flaw.

(c) Find the mean number of flaws per 1000 meter length of wire, the variance and the standard deviation.

(d) Generate the graph of the probability mass function for the number of flaws in 1000 meters of wire.

(e) Suppose you examine a 1000 meter length of wire. What is the probability that there is exactly 1 defect in the first 500 meters and exactly 2 defects in the second 500 meters of wire? What is the probability that there are exactly 3 defects anywhere in the 1000 meters of wire? Do your two answers “make sense”? Please explain.