Question

Problem 3-15 (Algorithmic) Telephone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (a) Find the probability of receiving 6 calls in a 5-minute interval. If required, round your answer to four decimal places. f(6) = (b) Find the probability of receiving 8 calls in 15 minutes. If required, round your answer to four decimal places. f(8) = (c) Suppose that no calls are currently on hold. If the agent takes 4 minutes to complete processing the current call, how many callers do you expect to be waiting by that time? If required, round your answer to one decimal place. Number of callers = What is the probability that no one will be waiting? If required, round your answer to four decimal places. The probability none will be waiting after 4 minutes is . (d) If no calls are currently being processed, what is the probability that the agent can take 2 minutes for personal time without being interrupted? If required, round your answer to four decimal places. The probability of no interruptions in 2 minutes is .

Answer 1

= 48 calls per hour.

(a)

5 minutes = (5/60) = 1/12 hours

Expected arrivals in five minutes = = 48*(1/12) = 4 calls per 5 minutes

The probability of 6 calls in 5 minutes is given by

=0.1042

f(6) = 0.1042

(b)

15 minutes = (15/60) = 1/4 hours = 0.25 hours

Expected arrivals in five minutes = = 48*(0.25) = 12 calls

The probability of 8 calls in 15 minutes is given by

=0.0655

=0.1042

f(8) = 0.1042

(c)

Expected number of calls waiting in 4 minutes = 48*(4/60) = 3.2

Number of callers = 3.2

The probability that no one will be waiting in 4 minutes is

=0.04076

The probability none will be waiting after 4 minutes is 0.0408.

(d)

No interruptions mean no calls in 2 minutes.

Expected number of calls in 2 minutes = 48*(2/60) = 1.6

The probability that no one will call in 2 minutes is

=0.20189

The probability of no interruptions in 2 minutes is 0.2019.