State University allows students and professors to access its central computer by modem. The university has 15 modem connections that can be used. When all modem connections are in use, the phone system can hold up to 10 callers waiting for a modem connection to become available. If all 15 modem connections are in use and 10 calls are already on hold, a new caller receives a busy signal. Calls to the modem pool follow a Poisson distribution and occur at an average rate of 60 calls per hour. The duration of each session with the mainframe is an exponential random variable with a mean of 15 minutes; therefore, each modem serves an average of Four callers per hour.

a. On average, how many callers are on hold waiting for a modem connection? second. On average, how long does a caller wait before receiving a modem connection?

b. What is the probability that a caller will receive a busy signal?

C. How many modem connections would the university need to add to its modem pool so that there is no more than a 1% chance that a caller will receive a busy signal?