Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6 planes arrive in the next minute is 0.05041.

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a fixed interval in a Poisson process is given by $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (mean) of occurrences in that interval, and $k$ is the number of occurrences. For $\lambda = 3$ and $k = 6$, the formula yields $P(6; 3) = \frac{e^{-3} 3^6}{6!} \approx 0.0504$, matching the provided probability.

Suppose That the Number of Airplanes Arriving at an Airport