Question

In: Math

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional...

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?

Solutions

Expert Solution

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.


Related Solutions

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional...
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Compute the probability of receiving one call in a 5-minute interval of time.   (to 4 decimals) b. Compute the probability of receiving exactly 13 calls in 15 minutes.   (to 4 decimals) c. Suppose no calls are currently on hold. If the agent takes 10 minutes to complete the current call, how many callers do you expect to be waiting by that time?...
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.a.Compute the probability of receiving one call in a 10 -minute interval of time.b.Compute the probability of receiving exactly11 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?What is the probability that none will be waiting?d. If no calls are...
Problem 3-15 (Algorithmic) Telephone calls arrive at the rate of 48 per hour at the reservation...
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...
Cars arrive at a parking lot at a rate of 20 per hour. Assume that a...
Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model is appropriate. Answer the following questions. No derivations are needed but justification of your answers are necessary. What assumptions are necessary to model the arrival of cars as a Poisson process? What is the expected number of cars that arrive between 10:00 a.m and 11:45 a. m? Suppose you walk into the parking lot at 10:15 a.m.; how long, on average,...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution. A. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function. B. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson. C. Compute the percent relative difference between the exact probability computed in...
People arrive at a party according to a Poisson process of rate 30 per hour and...
People arrive at a party according to a Poisson process of rate 30 per hour and remain for an independent exponential time of mean 2 hours. Let X(t) be the number of people at the party at time t (in hours) after it started. Compute E[X(t)] and determine how long it takes to have on average more than 40 people at the party.
Customers arrive at a local ATM at an average rate of 14 per hour. Assume the...
Customers arrive at a local ATM at an average rate of 14 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames. ​a) What is the probability that the next customer will arrive within the next 2 ​minutes? ​b) What is the probability that the next customer will arrive in more than 15 ​minutes? ​c) What is the probability that the next customer will...
Customers arrive at the rate of 100 per hour. The ticket seller averages 30 seconds per...
Customers arrive at the rate of 100 per hour. The ticket seller averages 30 seconds per customer. What is the average customer time in the system?
A) Phone calls arrive at a particular call center with an average of 12 every minute....
A) Phone calls arrive at a particular call center with an average of 12 every minute. The call center management want the maximum probability of having more calls than staff in any given minute being .2. How many staff are necessary to ensure this? Use Excel to help you find the answer. B) Consider the 1981 Super Bowl commercial from Schlitz involving a live taste test. Schlitz sponsored a live taste test for its beer during the half time of...
Students arrive at a local bar at a mean rate of 30 students per hour. Assume...
Students arrive at a local bar at a mean rate of 30 students per hour. Assume that the bouncer waits X (minutes) to card the next student. That is, X is the time between two students arriving at the bar. Then we know that X has approximately an exponential distribution. (a) What is the probability that nobody shows up within the 2 minutes after the previous customer? (b) What is the probability that the next student arrives in the third...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT