The local police department must write,on average,five tickets a day to keep department revenues at budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day.Interpret the value of the mean.
A) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
B) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.
C) The number of tickets that is written most often is 6.5 tickets per day.
D) The mean has no interpretation since 0.5 tickets can never be written.

Question

Quizplus · Accepted Answer

The mean of a Poisson distribution represents the expected or average number of events (in this case, tickets written) per unit of time (in this case, per day). Therefore, if the mean is 6.5 tickets per day, we expect on average 6.5 tickets to be written each day. Option A is incorrect because the Poisson distribution is not symmetric; it is skewed to the right, so most days will have fewer than 6.5 tickets written. Option C is incorrect because the mode of a Poisson distribution is not necessarily equal to the mean. Option D is incorrect because the mean can have a meaningful interpretation even if it is not a whole number; for example, we can interpret 6.5 as meaning we expect on average 6 or 7 tickets to be written, with some variability around that average.

The Local Police Department Must Write,on Average,five Tickets a Day