Refer to Exercise 4.

a. Find the probability that there are exactly 5 flaws in a 50 m length of cable.
b. Find the probability that there are more than two flaws in a 20 m length of cable.
c. Find the probability that there are no flaws in a 15 m length of cable.
d. Find the probability that the distance between two flaws is greater than 15 m.
e. Find the probability that the distance between two flaws is between 8 and 20 m.


(a) The mean distance between flaws is 12 m, so the mean number of flaws is 1?12 per meter. Let Xbe the number of flaws in a 50 m length. It follows that X~Poisson(25?6).



(b)Let X be the number of flaws in a 20m length. Then X~Poisson(5?3).



(c) Let X be the number of flaws in a 15m length. It follows that X~Poisson(5?4).



(d) Let D be the distance between two flaws.



(e) Let D be the distance between two flaws.

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