1. The number of cracks in a section of interstate highway that are significant

Question

1. The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of 2 cracks per mile. (a) What is the probability that there are no crack that require repair in 5 miles of highway? (b) what is the probability that at least one crack requires repair in ½ mile of highway? (c) Find the minimum number of cracks in 1/2 mile of highway so that the probability of this number or fewer cracks is at least 0.98. (d) If the number of cracks is related to vehicle load on the highway and some sections of the highway have a heavy load of vehicles whereas other sections carry a light load, what do you think about the assumption of a Poisson distribution for the cracks that require repair?

Explanation / Answer

a)

Average number of cracks in 5 mile highway = 10

Poisson Probability: P(X = 0) = 4.53999297624849E-05

b)

Average number of cracks in 0.5 mile highway = 1

Poisson Probability: P(X = 1) = 0.368

c)

3 cracks

Cumulative Probability: P(X < 3) = 0.981

d)

The poisson average of crack for the part of the highway having heavy load would be more than the one having light load

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