The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that exactly 8 customers will arrive in a one-hour period is 0.1366.

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a fixed interval of time in a Poisson distribution is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of events (8.60 in this case) and $k$ is the number of events of interest (8 customers). Plugging these values into the formula gives a result that matches the provided probability, confirming the statement is true.

The Number of Customers Who Arrive at a Fast Food