Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The average number of airplanes arriving per minute is three.The probability that exactly six planes arrive in the next minute is 0.0504.

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 of occurrence of the event per interval. Here, $\lambda = 3$ and $k = 6$. Plugging these values into the formula gives $P(6; 3) = \frac{e^{-3} 3^6}{6!} \approx 0.0504$, confirming the statement.

Suppose That the Number of Airplanes Arriving at an Airport