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 of 5tickets per day. Find the probability that exactly eight tickets are written on a randomly selected day from thisdistribution.
A) 0.065278
B) 0.005476
C) 0.003250
D) 0.000273

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a Poisson distribution is given by the formula $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (mean) of occurrence and $k$ is the number of occurrences. Here, $\lambda = 5$ and $k = 8$. Substituting these values into the formula gives $P(X=8) = \frac{e^{-5} 5^8}{8!}$, which calculates to approximately 0.065278.

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