The Poisson distribution defines the probability of k discrete and independent events occurring in a given time interval.
If λ = the average number of event occurring within the given interval, then
[tex]P(k \, events) = e^{-\lambda } ( \frac{\lambda ^{k}}{k!} )[/tex]
For the given problem,
λ = 6.5, average number of tickets per day.
k = 6, the required number of tickets per day
The Poisson distribution is
[tex]P(k \, tickets/day)=e^{-6.5} ( \frac{6.5 ^{k}}{k!} )[/tex]
The distribution is graphed as shown below.
Answer:
The mean is λ = 6.5 tickets per day, and it represents the expected number of tickets written per day.
The required value of k = 6 is less than the expected value, therefore the department's revenue target is met on an average basis.
