Question

Homework: Chapter 5 Save 6 of 6 (5 complete) HW Score: 85.71%, 12 of 14 pts Score: 0 of 2 pts 5.3.58 Question Help A new phone answering system for a company is capable of handling seven 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 three 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? The probability that more calls will arrive than the system can handle is (Round to four decimal places as needed.) Vi () More Enter your answer in the answer box and then click Check Answer. All parts showing Check Answer Clear All

Answer 1

We are given the mean arrival calls here as: 3/10 every minute that is 0.3 calls per minute. The handling capacity here is given as 7 calls in 10 minutes. Average call arrival is 3 calls per 10 minutes. Therefore for 10 minutes, the number of calls here could be modelled as:

X ~ Poisson (3)

Probability that more calls will arrive than the system can handle is computed using poisson probability function as:

P(X > 7) = 1- P(X<7)

P(X> 7) =1--3-3-3_

P(X>7) = 0.01190

Therefore 0.0119 is the required probability here.