The mean number of automobiles entering a mountain tunnel per two-minute period is one

Chapter 3, Problem 3.132

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QUESTION:

The mean number of automobiles entering a mountain tunnel per two-minute period is one. An excessive number of cars entering the tunnel during a brief period of time produces a hazardous situation. Find the probability that the number of autos entering the tunnel during a two-minute period exceeds three. Does the Poisson model seem reasonable for this problem?

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QUESTION:

The mean number of automobiles entering a mountain tunnel per two-minute period is one. An excessive number of cars entering the tunnel during a brief period of time produces a hazardous situation. Find the probability that the number of autos entering the tunnel during a two-minute period exceeds three. Does the Poisson model seem reasonable for this problem?

ANSWER:

Step 1 of 4

The average rate is  per two minute period,

Formula geometric probability is,

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