The call center of a major energy provider expects to be particularly busy during the early shift in the early Winter.

Question

The call center of a major energy provider expects to be particularly busy during the early shift in the early Winter. During the early shift calls arrive at a mean rate of 240 per hour and are believed to arrive at random.

(a) Explain briefly why it might be reasonable to expect these calls to arrive at random.

(b) What would be the probability distribution of the number of calls arriving during a five-minute period in the early shift? (There is no need to calculate any probabilities in this part of the question).

(c) Show (using probability tables or probability formulae) that the probability that there are more than 26 calls in a five-minute period is 0.0778. Show your working.

(d) Staffing levels during the early shift are such that they can cope with occasional peaks in arrivals, but service levels deteriorate rapidly when they experience a number of peaks close together. Continuing to assume that calls arrive at random, show that the probability that there are 6 or more five-minute periods in an hour in which the number of calls exceeds 26 is less than 1 in 1000. Show your working.

(e) Quiet periods only occur very rarely during the early shift in the call centre, so when gaps between calls exceed 2 minutes the management takes it as a signal of a telephone system failure and resets the system. What is the chance they reset the system unnecessarily in response to a 2 minute gap? Justify your method.

(f) You have seen in class how a Normal distribution can be used to approximate a Binomial distribution under certain conditions on n and p. (Remember that the Normal distribution was chosen to match the Binomial distribution in mean and standard deviation). A Normal distribution can also be used to approximate a Poisson distribution under certain conditions. By applying the same idea, use the Normal distribution to provide an approximate answer to part (c) above. Explain your method carefully.

(g) Suggest the conditions under which a Normal distribution can be used to approximate a Poisson distribution. Justify your answer.

Expert Solution

genius_generous answered 2 years ago

The length of incoming calls at the call center of a major telecommunication service provider follows...

The length of incoming calls at the call center of a major telecommunication service provider follows a Normal distribution with an average of 7.5 minutes. If the standard deviation of the distribution is 5 minutes, answer the following questions: (8 points) What is the probability that the length of an incoming call is longer than 9.5 minutes? What is the probability that the length of an incoming call is shorter than 6 minutes? What is the probability that the length...

Call Center Shift A Average Call Time Shift B Average Call Time Average Satisfaction Level Average...

Call Center Shift A Average Call Time Shift B Average Call Time Average Satisfaction Level Average Number of Employees 1 14 29 2 100 2 1 1 1 90 3 53 60 4 80 4 10 25 2 54 5 85 71 4 69 6 18 33 2 54 7 24 40 2 42 8 58 65 4 67 9 33 46 3 30 10 9 19 1 48 Use the z-score to determine which call centers, if any, should...

A computer call center is going to replace all of its incandescent lamps with more energy...

A computer call center is going to replace all of its incandescent lamps with more energy efficient fluorescent lighting fixtures. The total energy savings are estimated to be $1,875 per year, and the cost of purchasing and installing the fluorescent fixtures is $4,900. The study period is five years, and terminal values for the fixtures are negligible. What is the IRR of this investment? Express your answer in percent rounded to two decimal places. STEP BY STEP SOLUTION PLS NO...

During the early part of the last century, a prominent English lord spent a month each winter vacationing on a small island in the Indian Ocean

During the early part of the last century, a prominent English lord spent a month each winter vacationing on a small island in the Indian Ocean. He paid for his expenses by writing checks on his London bank account. So great was the impression of his lordship on the local inhabitants, that instead of cashing his checks, they held on to them dearly, and transferred them among themselves in settlement of transactions and for the payment of debts – that...

During the early part of the last century, a prominent English lord spent a month each winter vacationing on a small island in the Indian Ocean.

During the early part of the last century, a prominent English lord spent a month each winter vacationing on a small island in the Indian Ocean. He paid for his expenses by writing checks on his London bank account. So great was the impression of his lordship on the local inhabitants, that instead of cashing his checks, they held on to them dearly, and transferred them among themselves in settlement of transactions and for the payment of debts – that...

Question

The call center of a major energy provider expects to be particularly busy during the early shift in the early Winter.

Solutions

Expert Solution

Related Solutions

The length of incoming calls at the call center of a major telecommunication service provider follows...

Call Center Shift A Average Call Time Shift B Average Call Time Average Satisfaction Level Average...

A computer call center is going to replace all of its incandescent lamps with more energy...

During the early part of the last century, a prominent English lord spent a month each winter vacationing on a small island in the Indian Ocean

During the early part of the last century, a prominent English lord spent a month each winter vacationing on a small island in the Indian Ocean.

State the MAJOR steps for Malus domestica to harvest light energy and convert to sugar during...

State the MAJOR steps for Malus domestica to harvest light energy and convert to sugar during...

State the MAJOR steps for Malus domestica to harvest light energy and convert to sugar during...