Refer to Exercise 4.

a. Find the probability that there are exactly 5 flaws in a \(50 \mathrm{~m}\) length of cable.

b. Find the probability that there are more than two flaws in a \(20 \mathrm{~m}\) length of cable.

c. Find the probability that there are no flaws in a \(15 \mathrm{~m}\) length of cable.

d. Find the probability that the distance between two flaws is greater than \(15 \mathrm{~m}\).

e. Find the probability that the distance between two flaws is between 8 and \(20 \mathrm{~m}\).

Data From Exercise 4:

The distance between flaws on a long cable is exponentially distributed with mean \(12 \mathrm{~m}\).