You are calling your internet provider customer service with a complain about yo

Question

You are calling your internet provider customer service with a complain about your bill. When you are connected to a representative, it will be, with equal probability, somebody from the billing department, customer retention department or marketing department. When talking to a billing representative, the time until the issue is resolved is distributed uniformly from 10 to 20 minutes. Customer retention specialist will resolve you issue in exactly 2 minutes. Marketing person will rst discuss with you promotions and new offers (this time will be normally distributedwithaverage10 minutes and standard deviation 2) and then transfer you to a new representative, who will, again be from one of the three departments with equal probability. What is the expected time that you will spend on the phone?

Explanation / Answer

here probability of selecting each department =1/3

expected time that you will spend on the phone E(X)=expected time if you call billing department+expected time if you call customer retention+expected time if you call marketing department. =(1/3)*(10+20)/2+(1/3)*2+(1/3)*(10+E(X))

E(X) = 5+2/3+10/3+E(X)/3

2*E(X)/3 =27/3

E(X)=27/2 =13.5 minutes

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