Exhibit 5-15.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. Refer to Exhibit 5-15.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 the average arrival rate of customers is λ=2 customers/5 minutes, which means that the arrival rate for a 15 minute period would be λ=6 customers. Therefore, the parameter for the Poisson distribution is λ=6. The probability of exactly 7 customers entering the queue in a 15 minute period can be calculated using the Poisson probability formula:

P(X=7) = e^(-6) * 6^7 / 7!

where e is the base of the natural logarithm and 7! means 7 factorial (7 x 6 x 5 x 4 x 3 x 2 x 1).

P(X=7) = e^(-6) * 279936 / 5040
P(X=7) ≈ 0.1377

Therefore, the best choice is C (0.1377) as it is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period.