The university police department must write, on average, five tickets per day to keep department revenues atbudgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of6.5 tickets per day. Interpret the value of the mean.
A) If we sampled all days, the arithmetic average number of tickets written would be 6.5 tickets per day.
B) The number of tickets that is written most often is 6.5 tickets per day.
C) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets 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 rate at which events (in this case, tickets being written) happen per interval (in this case, per day). Therefore, if we sampled all days, the arithmetic average number of tickets written would indeed be 6.5 tickets per day.

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