A bank manager estimates that an average of two customers enters the tellers' queue every five minutes. Assume that the number of customers that enters the tellers' queue is Poisson distributed. What is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period?
A) 0.0034
B) 0.1033
C) 0.1377
D) 0.1606

Question

Quizplus · Accepted Answer

We know that $\lambda$, the average number of customers that enters the queue in a 5-minute period, is 2.

To find the probability that exactly 7 customers enter the queue in a 15-minute period, we need to use the Poisson distribution formula:

$$P(X=7) = \frac{e^{-\lambda}\lambda^x}{x!}$$

where x is the number of customers entering the queue, and $\lambda$ is the average rate of customers entering the queue.

Substituting the values, we get:

$$P(X=7) = \frac{e^{-2}\cdot 2^7}{7!} = 0.1377$$

Therefore, the answer is C.

A Bank Manager Estimates That an Average of Two Customers