WHAT IS THE AVERAGE NUMBER OF CUSTOMERS WHO ARE AT THE CHECKOUT DESK, EITHER WAITING OR CURRENTLY BEING SERVICED (WITHIN 1 CUSTOMER)?

11 May WHAT IS THE AVERAGE NUMBER OF CUSTOMERS WHO ARE AT THE CHECKOUT DESK, EITHER WAITING OR CURRENTLY BEING SERVICED (WITHIN 1 CUSTOMER)?

Atlantic
Video, a small video rental store in Philadelphia, is open 24 hours a day,
and due to its proximity to a major business school experiences customers
arriving around the clock. A recent analysis done by the store manager
indicates that there are 30 customers arriving every hour, with a standard
deviation of inter-arrival times of 2 minutes. This arrival pattern is
consistent and is independent of the time of the day. The checkout is
currently operated by one employee, who needs on average 1.7 minutes to check
out a customer. The standard deviation of this checkout time is 3 minutes,
primarily as a result of customers taking home different numbers of videos.

If
you assume that every customer rents at least one video (i.e. has to go to
the check-out), what is the average time a customer has to wait in line
before getting served by the check-out employee, not including the actual
check-out time (within 1 minute)?

1.
0 minutes

2.
5 minutes

3.
12 minutes

4.
20 minutes

5.
42 minutes

6.
63 minutes

7.
None of the above

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2.
Atlantic Video Company (2)(Points: 0.91)

If
there are no customers requiring checkout, the employee is sorting returned
videos, of which there are always plenty waiting to be sorted. How many
videos can the employee sort over an 8-hour shift (assume no breaks), if it
takes exactly 1.5 minutes to sort a single video?

1.
0 videos

2.
48 videos

3.
64 videos

4.
125 videos

5.
232 videos

6.
272 videos

7.
None of the above

3.
Atlantic Video Company (3)(Points: 0.91)

What
is the average number of customers who are at the checkout desk, either
waiting or currently being serviced (within 1 customer)?

1.
1 customer

2.
6 customers

3.
10 customers

4.
11 customers

5.
31 customers

6.
32 customers

7.
None of the above

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4.
Atlantic Video Company (4)(Points: 0.91)

Now
assume that 10% of the customers do not rent a cassette at all and therefore do
not have to go through checkout. What is the average time a customer has to
wait in line before getting served by the checkout employee, not including
the actual check-out time (within 1 minute)?

1.
1 minute

2.
5 minutes

3.
6 minutes

4.
11 minutes

5.
13 minutes

6.
32 minutes

7.
63 minutes

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5.
My-law.com Legal Services (5)(Points: 0.91)

My-law.com
is a recent start-up trying to cater to customers in search of legal services
who are intimidated by the idea of talking to a lawyer or simply to lazy for
entering a law office. Unlike traditional law firms, My-law.com allows for
extensive interaction between lawyers and their customers via telephone and
the internet. This process is used in the upfront part of the customer
interaction, largely consisting of answering some basic customer questions
prior to entering a formal relationship.

In
order to allow customers to interact with the firms lawyers, customers are
encouraged to send emails to my-lawyer@My-law.com. From there, the incoming
emails are distributed to the lawyer who is currently on call. Given the
broad skills of the lawyers, each lawyer can respond to each incoming
request.

Emails
arrive from 8am to 6pm at a rate of 10 emails per hour (coefficient or
variation for the arrivals is 1). At each moment in time, there is exactly
one lawyer on call, i.e. sitting at his/her desk, waiting for incoming
emails. It takes the lawyer, on average, 5 minutes to write the response
email. The standard deviation of this is 4 minutes.

What
is the average time a customer has to wait for the response to her email,
ignoring any transmission times?

1.
2 minutes

2.
2.5 minutes

3.
18 minutes

4.
25.5 minutes

5.
None of the above

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6.
My-law.com Legal Services (6)(Points: 0.91)

How
many emails will a lawyer have received at the end of a 10-hour day?

1.
10

2.
12

3.
100

4.
120

5.
None of the above