MGS 3100

Module 2 Sample Test Questions

1Simulation will always yield the best (best meaning maximum profit, etc.) solution to a problem.

TF

2If two different people run identical simulation models, they will obtain identical results.

TF

3A probability distribution is always referring to a discrete variable.

TF

4With small numbers of trials, simulations can be very sensitive to the initial conditions

TF

5A random number refers to:

  1. An observation from a set of numbers (i.e. the real numbers from 0-1), each of which is equally likely
  2. An observation selected at random from a normal distribution
  3. An observation selected at random from any distribution provided by the manager
  4. None of the above

6Consider the following simulation of a coin toss, with the experiment performed 3 times.

Experiment: Toss a coin 8 times and count the number of HEADS
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / # of Heads
0.498 / 0.746 / 0.044 / 0.511 / 0.218 / 0.783 / 0.121 / 0.869
0.139 / 0.547 / 0.490 / 0.336 / 0.462 / 0.476 / 0.332 / 0.052
0.493 / 0.694 / 0.792 / 0.678 / 0.740 / 0.517 / 0.619 / 0.042

AVERAGE =

Fill in the blanks in the table above. Write the rule you used in the space below.

7"All random numbers greater than 0.75 will be called Heads". What is wrong with the preceding rule as it applies to a coin toss simulation? Circle the correct response.

i)There will be too many "Heads" generated in the long run.

ii)There will be 75% "Tails", in the long run.

iii)The number of "Heads" will be 75% of all outcomes, in the long run.

iv)There is nothing wrong with the rule, if it is truly a fair coin.

8The RAND() function in Excel generates random numbers that range from ______to ______, with a ______distribution.

9Consider the following demand pattern for a product for the past 50 weeks.

Demand (Units) / Frequency (Weeks) / Prob / Cum Prob / Demand
18 / 11 / .22 / .22
19 / 16
20 / 15 / .30
21 / 8
Total / 50

Fill in the blanks in the table so that using the last two columns for a VLOOKUP statement will let you map random numbers to the correct demand level.

10The following table shows a portion of a simulation for a queuing system involving trucks. Fill in the blanks for truck numbers 8 and 10. The blank boxes have been highlighted.

Truck # / Arrival
Interval / Truck
Arrives at / Wait
Time / Service
Begins at / Loading
Time / Service
Ends at / Truck # / Last
Truck that
Left system / Trucks
in
System / Trucks
in
Queue
0 / 0
5 / 0.89 / 3.85 / 0.00 / 3.85 / 0.18 / 4.03 / 5 / 4 / 0 / 0
6 / 0.52 / 4.37 / 0.00 / 4.37 / 0.11 / 4.48 / 6 / 5 / 0 / 0
7 / 0.11 / 4.48 / 0.00 / 4.48 / 0.01 / 4.49 / 7 / 5 / 1 / 0
8 / 0.23 / 0.81 / 8
9 / 0.08 / 4.78 / 0.73 / 5.52 / 1.91 / 7.43 / 9 / 7 / 1 / 0
10 / 0.33 / 7.43 / 0.85 / 8.28 / 10 / 2 / 1

11To simulate a discrete variable, why do we compute cumulative probabilities?

12Since the result (in terms of a performance measure like profit) of a simulation and an expected value can be very similar, a reason to use simulation is becausesimulation can provide an indication of the variability of a decision

TF

13The all Washed-Up Car Wash has found a tremendous bargain on a new car waxing machine imported from the newly independent Republic of Lowenbrau. The only weak point is the special wax pump, which can be expected to fail relatively frequently and cannot be repaired. AWUCW can order up to five replacement pumps at a time, which would be delivered with the annual end of year shipment from Lowenbrau. They are available at no other time, and are expensive. If the wax pump fails and they have no replacement, they must stop using the machine until the next shipment arrives. The probabilities of breakdowns during any given year are given below:

Breakdowns per year / Probability
0 / 0.30
1 / 0.25
2 / 0.15
3 / 0.12
4 / 0.10
5 / 0.08
Sum / 1.00

In an average year, how many pumps can they expect to fail?

A)0

B)1.71

C)2.25

D)4.81

E)5.00

14The random number 0.57 has been selected. The corresponding observation, r, from the following discrete probability distribution would be:

r P(r)

0 0.30

1 0.20

2 0.40

3 0.10

A)0

B)1

C)2

D)3

E)None of the above

15The number of machine breakdowns in a day is 0, 1, or 2, with probabilities 0.6, 0.3, and 0.1, respectively. The following random numbers have been generated: 13, 10, 02, 18, 31, 19, 32, 85, 31, 94. Use these numbers to generate the number of breakdowns for 10 consecutive days. What proportion of these days had at least 1 breakdown?

A)0.2

B)0.3

C)0.4

D)0.5

E)0.6