During tax season, the IRS hires seasonal workers to help answer the questions of taxpayers who call a special 800 telephone number for tax information. Suppose that calls to this line occur at a rate of 60 per hour and follow a Poisson distribution. The IRS workers manning the phone lines can answer an average of 5 calls per hour with the actual service times following an exponential distribution. Assume that 10 IRS workers are available and, when they are all busy, the phone system can keep 5 additional callers on hold. a. What is the probability that a caller receives a busy signal?
b. What is the probability that a caller is put on hold before receiving service?
c. On average, how long must a caller wait before speaking with an IRS agent?
d. How many additional workers would be required if the IRS wants no more than a 5% chance of a caller receiving a busy signal?