On average, there are 12 potholes per mile on a particular stretch of the state

Question

On average, there are 12 potholes per mile on a particular stretch of the state highway. Suppose the potholes follow a Poisson distribution on the highway. a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway. (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability b. Find the probability of finding more than one pothole in a quarter-mile stretch of the highway. (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability

Explanation / Answer

= 12 per mile = 3 per quarter mile

P(X = x) = e- * x / x!

a) P(X < 2) = P(X = 0) + P(X = 1)

                  = e-3 * 30 / 0! + e-3 * 31 / 1!

                  = 0.1991

b) P(X > 1) = 1 - P(X < 1) = 1 - 0.1991 = 0.8009

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