A new phone answering system installed by the Ohio Power Company is capable of handling five calls every 10 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to two every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10-minute period more calls will arrive than the system can handle?
A) 0.174
B) 0.0812
C) 0.0166
D) 0.0233

Question

Quizplus · Accepted Answer

The probability that more than five calls will arrive in a 10-minute period, given a Poisson distribution with a mean ($\lambda$) of 2, can be calculated using the complement of the sum of probabilities of receiving 0, 1, 2, 3, 4, or 5 calls. The formula for the Poisson probability is $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $k$ is the number of occurrences (in this case, phone calls). The calculation for each of these probabilities and then summing them up and subtracting from 1 gives the probability of receiving more than 5 calls. The correct answer, after performing these calculations, is 0.0166.

A New Phone Answering System Installed by the Ohio Power