A customer service center receives phone calls at a rate of

A customer service center receives phone calls at a rate of 10 per hour. Let C be the number of phone calls received in a 4-hour shift. Let T be the amount time (in hours) of between 1st and 2nd calls. Assume that calls arrive independently.
a) Name the distribution and parameter(s) of C.
b) Name the distribution and parameter(s) of T.
c) Find the probability that there are between 50 and 52 calls (inclusive) between 2 pm and 6 pm.
d) A call came in to the customer service center at 2:05 pm, what is the probability that the next call comes in before 2:10 pm?

Solution