# Final

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```					Name:                                       Final                          Date: 5/16/2003

Instructions for this test:

1. Make sure to have your name on every page
2. This final test must be returned before Thursday 5:00PM, 22nd May 2003 (10% of
points will be removed if you submit after 5:00PM) in CC33. You will not get any
credit if it is late by a day.
3. Hand written test will not be accepted. It must be a typed test and it must be hard
copy. Emailing of your test is not considered as submission.
4. Include all formulas and steps required to solve a problem.
5. Total points of this test: 75.

Questions

1. A bank has one drive-in teller and room for one additional customer to wait.
Customers arriving when the queue is full, park and go inside the bank to transact
business. The time-between-arrivals and service time distributions are given
below:

Time between arrivals (minutes)          0       1       2    3        4          5
Probability                              0.09    0.17    0.27 0.20     0.15       0.12

Service Time (minutes)            1       2             3                4
Probability                       0.20    0.40          0.28             0.12

Simulate the operation of the drive-in teller for 10 new customers. The first of the
10 new customers arrives at a time determined at random. Start the simulation
with one customers being served, leaving at time 3, and one in the queue. How
many customers went into the bank to transact business? Make sure to show
simulation table (20 points).

2. A tool crib with one attendant serves a group of 10 mechanics. Mechanics work
for an exponentially distributed amount of time with mean 20 minutes, then go to
the crib to request a special tool. Service times by the attendant are exponentially
distributed with a mean of 3 minutes. If the attendant is paid \$6 per hour and the
mechanics \$10 per hour, would it be advisable to have second attendant? (10
points)

3.
a. Describe Runs up and Runs down algorithm (5 points).
b. Consider the first 50 two-digit values in example 7.7 of chapter 7 in
textbook. Can the hypothesis that the numbers are independent be rejected
on the basis of the length of runs above and below the mean, where alpha
= 0.05? (15 points)

1
Name:                                 Final                         Date: 5/16/2003

4. Use the multiplicative congruential method to generate a sequence of four three
digit random integers. Let X0 = 117, a = 43 and m = 1000 (10 points).

5. Describe (in detail) four steps involved in input modeling (15 points).
a. Note: Make sure to explain all sub topics involved in each step and also
provide examples. Refer to chapter 9 in textbook.

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