Customers arrive at a bus station at the rate of 5 per minute following Poisson distribution. What is the probability of 3 arrivals in a one-minute interval?
A) $\frac{e^{-5} 5^{3}}{3 !}$
B) $\frac{e^{-3} 5^{5}}{3 !}$
C) $\frac{e^{-5} 5^{3}}{5 !}$
D) $\frac{e^{5} 5^{-3}}{5 !}$

Question

Quizplus · Accepted Answer

The probability of $k$ arrivals in a Poisson distribution is given by $P(k) = \frac{e^{-\lambda} \lambda^{k}}{k !}$, where $\lambda$ is the average rate of arrivals per time period. Here, $\lambda = 5$ and $k = 3$, so the correct formula is $P(3) = \frac{e^{-5} 5^{3}}{3 !}$.

Customers Arrive at a Bus Station at the Rate of 5