Assume calls enter a 9-1-1 call center as a Poisson Process. If all operators are on a call, then the caller is placed into a queue that waits for the next available operator.
(a) How many calls are expected to be placed into the 9-1-1 call center from 9:00AM to 9:02AM, if calls are placed at a rate of 2 per minute? 1
(b) Assume at 9:00AM, all operators are available. Additionally, the call center has 5 operators and assume each call lasts exactly 2 minutes. What is the probability that a caller who calls between 9:00AM and 9:02AM will be placed into the queue given that the rate of calls is 2 per minute?
(c) Using the information from part (b), what is the minimum number of operators that need to be working during 9:00AM - 9:02AM to ensure that all calls are handled with at least 96% certainty?
I figured out part a), but I do not know how to approach part b and c. For part b) do I need to do a conditional probability?