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Poisson Distribution and Interpretation of the Mean

The local police department must write on average 5 tickets a day to keep department revenue at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Which of the following statements is the best interpretation of the value of the mean?

A. The number of tickets that is written most often is 6.5 tickets per day

B. Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written

C. If we sampled all days the arithmetic average or expected number of tickets written would be 6.5 tickets per day

D. The mean has no interpretation since 0.5 tickets can never be written; it must be a whole number

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The Poisson distribution is used to model the number of events occurring within a ...

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This solution involves a brief explanation for Poisson distribution and interpretation of the mean.