Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

Cars reach a fuel station randomly, with a steady mean arrival rate of 13.5 per hour.
(a)[3]

Find the probability that over 4 cars arrive in a 20-minute interval.

(b)[4]

Use an approximating distribution to determine the probability that the number of cars arriving in a 12-hour period lies between 150 and 160 inclusive.

(c)[3]

Find the probability that, in a 10-minute period, the total number of cars and trucks arriving at the fuel station is greater than 3 and less than 7.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Takes $\lambda = 4.5$

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