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?

e) Given that there are 5 calls in the first 20 minutes, what is the probability that all 5 calls are within the first 10 minutes?

f) What is the expected total number of calls received within 2 consecutive 4-hour shifts?

Solution

a) C~poission with parameter lamda=4*10=40..

b) T~uniform distribution[0,6]

c) P(50<C<52)=0.024571

d) P(0<T<5)=0.83