2 The number of cars passing a checkpoint during 200 periods of 5 minutes is recorded. Number of cars 2 3 4 5 6 7 8 > 9 Frequency 36 7 21 30 41 29 21 11 4 a Calculate the mean and the variance of the data. b Explain why the results in part a suggest that a Poisson distribution may be a suitable model for the number of cars passing the checkpoint in a 5-minute period. c Using a suitable value for à, estimate the probability that no more than 2 cars will pass the checkpoint in a given 5-minute period. d Compare your answer to part e with the relative frequency of obtaining no more than 2 cars from the sample.

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