Question

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 8.9. Find the probability that exactly four tickets are written on a randomly selected day.

Answer 1

Answer:

3.566%

Step-by-step explanation:

The probability formula for a poisson distribution is:

$P( k )=\frac{\lambda^{k}e^{-\lambda}}{k!}$

λ is the average of events

e is the euler's number

k is the number of events you want to know the probability

For this :

λ = 8.9 (on average the number of tickets is 8.9 per day)

k = 4 (you need to find the probability that exactly 4 tickets are written per day)

$P( k=4 )=\frac{8.9^{4}e^{-8.9}}{4!}=0,03566 =3.566\%$