A bank manager estimates that an average of two customers enter the tellers' queue every five minutes. Assume that the number of customers that enter the tellers' queue is Poisson distributed. What is the probability that exactly three customers enter the queue in a randomly selected five-minute period?
A) 0.0902
B) 0.1804
C) 0.2240
D) 0.2707

Question

Quizplus · Accepted Answer

We are given that the number of customers that enter the tellers' queue is Poisson distributed with an average of two customers every five minutes. This means that the parameter λ of the Poisson distribution is equal to 2. We want to find the probability that exactly three customers enter the queue in a randomly selected five-minute period. We can use the Poisson probability distribution to calculate this probability:

P(X = 3) = e^(-λ) * λ^3 / 3! = e^(-2) * 2^3 / 3! ≈ 0.1804

Therefore, the answer is B.

A Bank Manager Estimates That an Average of Two Customers