Compute Probabilities of a Poisson Random Variable
-The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 5. Find the probability that exactly three road construction projects are currently taking place in this city.
A) 0.140374
B) 0.051862
C) 0.272887
D) 0.100819

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 mean number of events. Here, $\lambda = 5$ and $k = 3$, so $P(X=3) = \frac{e^{-5} 5^3}{3!} = 0.140374$.