Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour.What is the probability that in the next hour there will be exactly 12 arrivals?
A)0.0000
B)0.0661
C)0.7500
D)0.1322

Question

Quizplus · Accepted Answer

The probability of exactly $k$ arrivals in a Poisson distribution is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean arrival rate and $k$ is the number of arrivals. Here, $\lambda = 16$ and $k = 12$. Plugging these values into the formula gives $P(X=12) = \frac{e^{-16} 16^{12}}{12!}$, which calculates to approximately 0.0661.

Arrivals at a Fast-Food Restaurant Follow a Poisson Distribution with a Mean