Question

The Sutton police department must write, on average, 6 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.
-The mean has no interpretation.
-The expected number of tickets written would be 6.5 per day.
-Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
-The number of tickets that is written most often is 6.5 tickets per day.

Answer 1

The expected number of tickets written would be 6.5 per day.

Explanation:

Given that the Sutton police department must write, on average, 6 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.

This means population parameter i.e. expected value of tickets a day is 6.5

Option I is wrong, because 6.5 is the parameter of Poisson distribution for number of tickets

Option III is wrong because mean is the overall average and hence need not be balanced by exactly half.

Option IV is wrong because mean is the expected value and so we cannot say more than 6.5 tickets

Only correct option is option 2.

The expected number of tickets written would be 6.5 per day.