In: Math
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
a. Compute the probability of receiving four calls in a 5-minute interval of time.
b. Compute the probability of receiving exactly 9 calls in 15 minutes.
c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?
d. Suppose, no calls are currently on hold, If the agent takes 5 minutes to complete the current call, what is the probability that no callers will be waiting?
e. If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?
We would be looking at the first 4 parts here.
The number of calls in a 5 minute interval is modelled here as:
The probability of receiving 4 calls in a 5-minute interval is computed here as:
Therefore 0.1954 is the required probability here.
b) For 15 minutes, average number of calls would be 4*3 = 12 as there were average 4 calls in a 5 minute interval. Therefore the number of calls in a 15 minute interval could be modelled here as:
Probability of exactly 9 calls in 15 minutes could be computed here as:
Therefore 0.0873 is the required probability here.
c) The expected number of callers to be waited is computed here
as:
= Average number of calls in a 5 minute interval
= 4
Therefore 4 is the expected number of callers here
d) Probability of no caller waiting in the 5 minute interval is computed here as:
Therefore 0.0183 is the required probability here.