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 five 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 five 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?