Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is four. The probability that three customers will arrive in the next two hours is:
A) less than or equal to 0.015.
B) greater than 0.015 but less than or equal to 0.020.
C) greater than 0.020 but less than or equal to 0.025.
D) greater than 0.025.

Question

Quizplus · Accepted Answer

The average number of customer arrivals in two hours is 8 (since 4 customers arrive per hour on average). Using the Poisson distribution formula $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (8 for two hours) and $k$ is the number of occurrences (3 customers), we find $P(X=3) = \frac{e^{-8} 8^3}{3!}$. This calculation results in a probability greater than 0.025, making option D correct.

Customers Arrive According to a Poisson Distribution