The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson
Distribution with a mean of 8.5. Interpret the value of the mean.
A)The mean has no interpretation since 0.5 ticket can never be written.
B)On half of the days less than 8.5 tickets are written and on half of the days have more than 8.5 tickets are written.
C)The number of tickets that is written most often is 8.5 tickets per day.
D)If we sampled all days, the arithmetic average number of tickets written would be 8.5 tickets per day.

Question

Quizplus · Accepted Answer

The mean of a Poisson distribution represents the average rate at which events (in this case, tickets being written) happen over a specified interval. Therefore, an average of 8.5 tickets written per day means that over a long period, if you were to calculate the arithmetic average of tickets written each day, it would converge to 8.5.

The University Police Department Must Write, on Average, Five Tickets