Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If a single teller is used, find:

The probability that the bank is empty.

Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If a single teller is used, find:

The average time in the line.

Janson’s Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential.

The cost of the clerk is $\$ 10$ per hour, but because of lost goodwill and sales, Janson's loses about $\$ 25$ per hour of customer time spent waiting for the clerk to take an order.

Pamela Janson is considering adding a second clerk to take calls. The store's cost would be the same $\$10$ per hour. Should she hire another clerk? Explain your decision.

Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If a single teller is used, find:

The average number in the line.

Janson’s Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential.

The cost of the clerk is $\$ 10$ per hour, but because of lost goodwill and sales, Janson's loses about $\$ 25$ per hour of customer time spent waiting for the clerk to take an order.

What is the average number of customers waiting to place an order?

Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only $l$ order at a time.

Suppose a second server is added and the 2 servers act independently, with each taking an average of 2 minutes. What would be the average time a student is in the system?

Who Is Responsible? Deborah goes to the bank to cash her payroll check for $\$ 160$. At the bank, the teller accidentally gives Deborah $180. Deborah instantly notices the error but puts the money into her wallet and leaves the bank.

Is not telling the bank teller that she gave you too much money the same as stealing?

Give three examples of unethical behavior involving lean operations, and state the relevant ethical principle that would be violated.

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the percentage of time that Rich is busy.

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich's service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.

Find the average time a customer waits until it is his or her turn.

A survey of the entering MBA students at a university in the United States categorized the country of origin of the students, as noticed in the table.

The same university reported the following data on the gender of their students in their two MBA programs.

a) What percent of all MBA students are women?

A survey of the entering MBA students at a university in the United States categorized the country of origin of the students, as noticed in the table.

The same university reported the following data on the gender of their students in their two MBA programs.

d) Do you see proof of an association between the Type of MBA program and the percentage of women students? If so, why do you believe this might be true?

A survey of the entering MBA students at a university in the United States categorized the country of origin of the students, as noticed in the table.

f) Do you think that origin of the MBA student is independent of the MBA program? Explain.

Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on average $\lambda=3$ per 8-hour workday (approximately Poisson in nature). The crew can service an average of $\mu=8$ machines per workday, with a repair time distribution that resembles the negative exponential distribution.

What is the average downtime for a broken machine?