Question

The potholes on a major highway in the city of Detroit has a Poisson distribution with a rate of 3 per mile. What is the probability that there are less than 6 potholes over a randomly selected 2-mile segment of the highway?

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Answer 1

For a Poisson Distribution

distance (d) = 2
Since we know that for poisson distribution

a) x = 6
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X < 6) = 0.00247875 + 0.01487251 + 0.04461754 + 0.08923508 + 0.13385262 + 0.1606
P(X < 6) = 0.4457
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