The number of flaws in a certain type of lumber follows a Poisson distribution with a rate of 0.45 per linear meter.
a. What is the probability that a board 3 meters in length has no flaws?
b. How long must a board be so that the probability it has no flaw is 0.5?
(a) Let X be the number of flaws in a 3-meter board. Since the mean number of flaws is 0.45 per meter, X ~ Poisson(1.35).
(b) Let n be the length in meters needed so that the probability of no flaw is 0.5. Then X ~ Poisson(0.45n), and
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