Question

4. Phone calls arrive at the rate of 48 per hour at the reservation desk for Varig Airlines. a. Find the probability of receiving three calls in a five-minute interval time. b. Find the probability of receiving exactly 10 calls in 15 minutes. c. Suppose no calls are currently on hold. If the agent takes five minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting? d. If no calls are currently being processed, what is the probability that the agent can take three minutes for personal time without being interrupted by a call?

Answer 1

a) expected calls in 5 minute =48*5/60=4=

therefore robability of receiving three calls in a five-minute interval time =P(X=3) =e^-44³/3! =0.1954

b) expected calls in 15 minute =48*15/60=12=

probability of receiving exactly 10 calls in 15 minutes =P(X=10) =e^-1212¹⁰/10! =0.1048

c)expeted  to be waiting by that time =48*5/60=4=

probability that none will be waiting =P(X=0) =e^-44⁰/0! = 0.0183

d) for 3 mimutes expected call =48*3/60=2.4

probability that no call will come in 3 minutes =e^-2.4*2.4⁰/0! =0.0907