Consider the following to answer the question(s) below:
The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5 minute period,
-What is the probability that no more than 2 customers will arrive in a 5 minute period?
A) 0.0005
B) 0.1246
C) 0.0028
D) 0.6767
E) The answer cannot be determined with the given information.

Question

Quizplus · Accepted Answer

The Poisson distribution is used when we want to know the probability of a certain number of events occurring in a fixed time interval when the events are occurring randomly and independently. In this case, the average rate of arrival is given as 2 customers per minute. Thus, the parameter λ for a 5-minute period will be 2*5=10. We need to find the probability that no more than 2 customers will arrive in a 5-minute period which translates to finding P(X ≤ 2) where X is a Poisson variable with mean λ =10. Using the Poisson distribution formula, we get:

P(X ≤ 2) = e^(-λ) * ( λ^0/0! + λ^1/1! + λ^2/2!)
           = e^(-10) * (1 + 10+ 50/2)
           = 0.0028 (rounded to 4 decimal places)

Thus, the probability of no more than 2 customers arriving in a 5-minute period is 0.0028 or approximately 0.3%. So, the correct choice is (C).

Consider the Following to Answer the Question(s) Below