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 7.5. Interpret the value of the mean.
A) If we sampled all days, the arithmetic average number of tickets written would be 7.5 tickets per day.
B) The number of tickets that is written most often is 7.5 tickets per day.
C) On half of the days less than 7.5 tickets are written and on half of the days have more than 7.5 tickets are written.
D) The mean has no interpretation since 0.5 ticket can never be written.

Question

Quizplus · Accepted Answer

The mean of a Poisson distribution represents the average number of events (tickets) expected to occur in a fixed interval (per day). Here, it indicates that, on average, 7.5 tickets are written per day.

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