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) Find the probability that there are between 50 and 52 calls (inclusive) between 2 pm and 6 pm.

b) 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?

c) 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?

d) 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