Assignment task: Calls arrive at James Hamann's hotel switchboard at a rate of 2.5 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation:
a) The probability that the operator is busy = 5.00). (Round your response to two decimal places.)
b) The average time that a caller must wait before reaching the operator - 1 minutes (Round your response to two decimal places.
c) The average number of calls waiting to be answered = calls (Round your response to two decimal places.)