Suppose that the flaws along magnetic tape follow a Poisson distribution with a mean of 0.2 flapper meter. Let X denotes the distance between two successive flaws.
a) What is the mean of X?
b) What is the probability that there are no flaws in 10 consecutive meters of tape?
c) Does your answer to part b) change if the 10 meters are not consecutive?
d) How many meters of tape needed to be inspected so that the probability that at least one flaw is found is 90%?
e) What is the probability that the first time the distance between two flaws exceeds 8 meters is at the fifth flaw?
f) What is the mean number of flaws before a distance between two flaws exceeds 8 meters?