The distance between consecutive flaws on a roll of sheet aluminum is exponentially distributed with a mean distance of three meters. a. what is the mean number of flaws per meter? b. what is the probability that we inspect the next six meters before finding a flaw? c. what is the probability that a five meter length of aluminum contains exactly two flaws?

Part a:

Given that the mean distance between consecutive flaws on a roll of sheet aluminum is 3 meters, thus the rate parameter (the mean number of flaws per meter) is given by 1 divided by the mean distance = 1 / 3 = 0.333

Part b:



Thus,



Therefore, the probability that we inspect the next six meters before finding a flaw is 0.1353.

Part c:

In a 5 metre length of aluminium, the mean distance between consecutive flaws is given by 5 x 1/3 = 5/3.

The probability that the five meter length of aluminum contains exactly two flaws is given by the poisson distribution with a mean of 5/3.