Compute Probabilities of a Poisson Random Variable
-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 5.2 tickets per day. Find the probability that exactly nine tickets are written on a randomly selected day from this distribution.
A) 0.042261
B) 0.001393
C) 0.000945
D) 0.000031

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a Poisson distribution is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of events. Here, $\lambda = 5.2$ and $k = 9$. Substituting these values into the formula gives $P(X=9) = \frac{e^{-5.2} \cdot 5.2^9}{9!}$, which calculates to approximately 0.042261, making option A correct.