The rate at which people pull into a gas station follows a Poisson Distribution

Question

The rate at which people pull into a gas station follows a Poisson Distribution with an average of 5 cars every 30 minutes. Find expressions for the following probabilities: (1) The probability that exactly 10 cars arrive in the first 30 minutes after opening. (2) The probability that the 5th car pulls in more than 30 minutes after opening. (3) The probability that the 5th car pulls in between 25 and 30 minutes after opening. (4) The probability that the 8th car pulls in exactly 30.00...minutes after opening. Your answers for (1) and (2) can be left as sums, but you should produce a decimal answer for (c) and (d).

Explanation / Answer

We would have to calculate with the following formula:-

P(x; ) = (e-) (x) / x!

1) P(X=10)=0.0181

2) P(X=4)=0.1754

3) P(X=5)=0.1754

4) P(X=7)=0.1044

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