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The transportation and public works department is in an effort to "plug" the holes in the...

The transportation and public works department is in an effort to "plug" the holes in the country's roads, so it has brigades dedicated to this task. Assume that on secondary roads the number of holes follows a Poisson distribution with an expected value of 5 holes per km of road.

a) Calculate the probability that the brigade has to cover more than 8 holes in a km of road selected at random

b) If the brigade serves 20 independent sections of one km during the month,
I. What is the expected number of holes that will have been covered at the end of the month?


II. What is the probability that less than 5 of the 20 sections have more than 8 holes each?

c) After finishing a particular hole, part of the brigade decides to walk to the next hole,
I. What is the probability that they will have to walk more than 200m?

II. If they have walked 100m without finding a hole, what is the probability that they will need to walk 200m more?

Math   Statistics-And-Probability   
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