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A B C D E F G H I J K L M N O
Coin-Flipping Game
Required Difference 3 Distribution of Coin Flips
Cash At End of Game $8 Probability
Cumulative
Result
0.5 0Heads
Summary of Game 0.5 0.5 Tails
Number of Flips 11
Winnings -$3
Number Number
Play of Flips Winnings Play of Flips Winnings
Random Total Total 11 -3 11 -3
Flip Number Result Heads Tails Stop? 115 -7 113 -5
10.2484 Heads 1 0 2 3 5 2 11 -3
20.6730 Tails 1 1 3 5 3 3 17 -9
30.5281 Tails 1 2 4 5 3 4 13 -5
40.7452 Tails 1 3 5 15 -7 517 -9
50.0414 Heads 2 3 6 13 -5 6 3 5
60.5055 Tails 2 4 7 5 3 7 5 3
70.4280 Heads 3 4 8 3 5 8 7 1
80.6195 Tails 3 5 9 7 1 9 5 3
90.2812 Heads 4 5 10 5 3 10 3 5
10 0.6233 Tails 4 6 11 11 -3 11 3 5
11 0.7813 Tails 4 7 Stop 12 3 5 12 11 -3
12 0.8905 Tails 4 8 NA 13 7 1 13 11 -3
13 0.0205 Heads 5 8 NA 14 7 1 14 15 -7
14 0.3349 Heads 6 8 NA 15 9-1
15 0.4593 Heads 7 8 NA Average: 7.429 0.571 16 9-1
16 0.7559 Tails 7 9 NA 17 5 3
997 3 5
998 11 -3
999 3 5
1000 5 3
Average: 8.972 -0.972
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A B C D E F G H I
Random Number of Number of
Flip Number Result Replication Heads Replication Heads
1 0.5455 Tails 2 2
2 0.4768 Heads 1 2 1 0
3 0.0344 Heads 2 2 2 1
3 2 3 3
Total Number of Heads = 2 4 1 4 1
5 1 5 2
6 1 6 1
7 2 7 1
8 1 8 3
9 1
10 0
798 1
799 2
800 1
Number with 0 heads = 96
Number with 1 head = 302
Number with 2 heads = 286
Number with 3 heads = 116
If Clear, Prob(Stays Clear) = 0.8
If Rain, Prob(Stays Rain) = 0.6
Random
Day Number Weather
Clear
10.4098 Clear
20.5221 Clear
30.1275 Clear
40.9282 Rain
50.6193 Clear
60.7496 Clear
70.5620 Clear
80.6473 Clear
90.8297 Rain
10 0.4973 Rain
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A B C D E
Simulated Tosses
Toss Die 1 Die 2 Sum
1 5 5 10
2 1 3 4
3 2 4 6
4 6 4 10
5 3 6 9
6 2 4 6
7 5 4 9
8 4 1 5
9 4 3 7
10 5 5 10
11 4 1 5
12 5 4 9
13 5 1 6
14 4 1 5
15 2 4 6
16 3 4 7
17 2 1 3
18 1 5 6
19 6 4 10
20 5 5 10
21 6 4 10
22 6 6 12
23 6 5 11
24 4 1 5
25 2 1 3
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A B C D E F G
Random Distribution of
Day Number Demand Demand
10.5019 4 Probability Cumulative Demand
20.5926 40.16 0 2
30.7080 40.28 0.16 3
40.5172 40.32 0.44 4
50.7379 40.20 0.76 5
60.2461 30.04 0.96 6
70.9155 5
297 0.5997 4
298 0.8325 5
299 0.4670 4
300 0.5109 4
Average = 3.833
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A B C
Random Service
Day Number Time
10.6873 6.436
20.8319 7.160
30.3156 4.578
40.7222 6.611
50.7595 6.797
60.3725 4.863
497 0.3427 4.713
498 0.9448 7.724
499 0.8457 7.228
500 0.5801 5.901
Average = 5.443
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A B C D E
Complimentary Complimentary
Random Service Random Service
Day Number Time Number Time
10.1052 0.263 0.8948 1.825
20.3455 0.864 0.6545 1.424
30.6952 1.492 0.3048 0.762
40.2132 0.533 0.7868 1.645
50.1428 0.357 0.8572 1.762
60.3317 0.829 0.6683 1.447
70.9332 1.889 0.0668 0.167
297 0.2309 0.577 0.7691 1.615
298 0.5871 1.312 0.4129 1.022
299 0.3674 0.919 0.6326 1.388
300 0.1518 0.380 0.8482 1.747
Average = 1.098 1.095
Overall Average = 1.097
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A B C D E F G H
Mean Interarrival Time = 5 hours
Size of Crew = 4
Mean Service Time = 2 hours
Average Time in Line (Wq) = 0.6 hours
Average Time in System (W) = 2.6 hours
Time Time Time Time Time
Customer Interarrival of Service Service Service in in
Arrival Time Arrival Begins Time Ends Line System
14.6 4.6 4.6 2.2 6.8 0.0 2.2
29.6 14.2 14.2 2.0 16.2 0.0 2.0
32.4 16.6 16.6 2.3 19.0 0.0 2.3
41.9 18.6 19.0 3.9 22.8 0.4 4.3
51.9 20.5 22.8 3.8 26.7 2.4 6.2
98 23.2 461.2 461.2 3.4 464.6 0.0 3.4
99 3.8 465.1 465.1 3.6 468.7 0.0 3.6
100 2.4 467.5 468.7 3.2 471.9 1.2 4.4
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 1 Point
Estimate Low High
Interarrival Times L = 2.6400238 2.391023309 2.889024283
Distribution = Exponential
Lq = 1.84604969 1.608885509 2.083213873
Mean = 5 W = 13.1728145 12.0696828 14.27594616
5
Wq = 9.21115565 8.123435323 10.29887598
Service Times
P0 = 0.2060259 0.189913768 0.222138023
Distribution = Uniform
P1 = 0.21033483 0.19666573 0.224003924
Minimum Value = 0
P2 = 0.17681767 0.166556409 0.187078933
Maximum Value = 8
P3 = 0.129046 0.120983504 0.137108487
P4 = 0.09237515 0.0840719 0.10067841
Length of Simulation Run
P5 = 0.05972938 0.052306386 0.067152364
Number of Arrivals = 10,000
P6 = 0.04061194 0.033735507 0.047488372
P7 =0.02570094 0.019924133 0.031477739
P8 = 0.01952973 0.014201062 0.024858396
P9 = 0.01383571 0.008578989 0.019092438
P10 = 0.00887497 0.004710957 0.013038973
95% Confidence Interval
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 1 Point
Estimate Low High
Interarrival Times L = 1.17865593 1.111741567 1.245570292
Distribution = Exponential
Lq = 0.58142685 0.524764999 0.638088703
Mean = 5 W = 5.91918526 5.65053463 6.18783588
5
Wq = 2.9199134 2.666936281 3.172890524
Service Times
P0 = 0.40277092 0.389560579 0.415981265
Distribution = Uniform
P1 = 0.28793502 0.280079418 0.295790626
Minimum Value = 0
P2 = 0.16180994 0.155142676 0.168477212
Maximum Value = 6
P3 = 0.07967267 0.073660996 0.08568435
P4 = 0.03651699 0.031748426 0.041285556
Length of Simulation Run
P5 = 0.01757122 0.013322806 0.02181963
Number of Arrivals = 10,000
P6 = 0.00761098 0.00515633 0.010065639
P7 =0.00287097 0.001559445 0.0041825
P8 = 0.00155877 0.000478633 0.002638915
P9 = 0.00102093 0.000143421 0.001898433
P10 = 0.00053959 -4.99843E-05 0.001129168
95% Confidence Interval
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 1 Point
Estimate Low High
Interarrival Times L = 0.58179891 0.557903926 0.605693887
Distribution = Exponential
Lq = 0.18464567 0.168481455 0.200809875
Mean = 5 W = 2.91732338 2.835376625 2.999270141
5
Wq = 0.92587165 0.855487569 0.996255741
Service Times
P0 = 0.60284676 0.593327724 0.612365793
Distribution = Uniform
P1 = 0.26540635 0.259908321 0.270904384
Minimum Value = 0
P2 = 0.0936247 0.088999592 0.098249817
Maximum Value = 4
P3 = 0.02737279 0.024387888 0.030357684
P4 = 0.00779303 0.00605179 0.009534275
Length of Simulation Run
P5 = 0.00208646 0.00127293 0.002899985
Number of Arrivals = 10,000
P6 = 0.00067048 0.000184955 0.001156013
P7 =0.00019793 -2.48982E-05 0.00042076
P8 = 1.4939E-06 -1.43181E-06 4.41962E-06
P9 = 0 0 0
P10 = 0 0 0
95% Confidence Interval
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A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results Range Name Cell
l = 0.2 (mean arrival rate) L = 2.933333333 LG4
1/m = 4 (expected service time)
Lq = 2.133333333 Lambda C4
s= 2.3094011 (standard deviation) Lq G5
s = 1 (# servers) W = 14.66666667 OneOverMu C5
Wq = 10.66666667 Rho G10
sC7
r = 0.8 Sigma C6
WG7
P0 = 0.2 Wq G8
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A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results Range Name Cell
l = 0.2 (mean arrival rate) L = 1.2 LG4
1/m = 3 (expected service time)
Lq = 0.6 Lambda C4
s= 1.7320508 (standard deviation) Lq G5
s = 1 (# servers) W = 6 OneOverMu C5
Wq = 3 Rho G10
sC7
r = 0.6 Sigma C6
WG7
P0 = 0.4 Wq G8
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A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results Range Name Cell
l = 0.2 (mean arrival rate) L = 0.577777778 LG4
1/m = 2 (expected service time)
Lq = 0.177777778 Lambda C4
s= 1.1547005 (standard deviation) Lq G5
s = 1 (# servers) W = 2.888888889 OneOverMu C5
Wq = 0.888888889 Rho G10
sC7
r = 0.4 Sigma C6
WG7
P0 = 0.6 Wq G8
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 2 Point
Estimate Low High
Interarrival Times L = 1.78757206 1.726441349 1.848702773
Distribution = Translated Exponential
Lq = 0.28220656 0.241680028 0.322733085
Minimum Value = 0.5 W = 1.79878512 1.747588762 1.84998147
Mean = 1
Wq = 0.28397678 0.244772435 0.32318112
Service Times
P0 = 0.07738102 0.069798855 0.084963186
Distribution = Erlang
P1 = 0.33987245 0.324592313 0.355152593
Mean = 1.5
P2 = 0.37038029 0.359243093 0.381517479
k = 4
P3 = 0.15923981 0.147308796 0.171170825
P4 = 0.0402521 0.032237042 0.048267158
Length of Simulation Run
P5 = 0.00942833 0.005068991 0.01378767
Number of Arrivals = 5,000
P6 = 0.00305244 0.000233056 0.005871825
P7 =0.00039356 -0.000134342 0.00092146
P8 = 0 0 0
P9 = 0 0 0
P10 = 0 0 0
95% Confidence Interval
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 3 Point
Estimate Low High
Interarrival Times L = 1.504601 1.471382686 1.537819251
Distribution = Translated Exponential
Lq = 0.0143989 0.010570703 0.018227099
Minimum Value = 0.5 W = 1.5180755 1.495626801 1.540524241
Mean = 1
Wq = 0.0145279 0.010727933 0.018327771
Service Times
P0 = 0.112177 0.103577706 0.120776216
Distribution = Erlang
P1 = 0.4046378 0.392449367 0.416826253
Mean = 1.5
P2 = 0.3639914 0.353062436 0.374920422
k = 4
P3 = 0.1056003 0.097335384 0.11386524
P4 = 0.0127881 0.009713729 0.015862418
Length of Simulation Run
P5 = 0.0008054 0.000273786 0.001337042
Number of Arrivals = 5,000
P6 = 0 0 0
P7 =0 0 0
P8 = 0 0 0
P9 = 0 0 0
P10 = 0 0 0
95% Confidence Interval
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 2 Point
Estimate Low High
Interarrival Times L = 2.2852618 2.151379363 2.41914419
Distribution = Translated Exponential
Lq = 0.6238658 0.509969808 0.737761839
Minimum Value = 0.5 W = 2.0664812 1.955490349 2.17747197
Mean = 0.9
Wq = 0.5641397 0.463906706 0.664372761
Service Times
P0 = 0.0456694 0.039854091 0.051484635
Distribution = Erlang
P1 = 0.2472653 0.228502346 0.266028296
Mean = 1.5
P2 = 0.3416445 0.322145294 0.361143622
k = 4
P3 = 0.2069829 0.191836287 0.222129571
P4 = 0.0926205 0.078093733 0.107147361
Length of Simulation Run
P5 = 0.0432628 0.028218881 0.05830673
Number of Arrivals = 5,000
P6 = 0.0149182 0.007216274 0.022620095
P7 =0.0049373 0.00059847 0.009276032
P8 = 0.0017697 -0.000692721 0.004232024
P9 = 0.0005594 -0.000522109 0.001640977
95% Confidence Interval
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A B C D E F G H
Template for Queueing Simulation
Data Results
Number of Servers = 3 Point
Estimate Low High
Interarrival Times L = 1.6572945 1.622102655 1.692486433
Distribution = Translated Exponential
Lq = 0.02092 0.015617543 0.02622253
Minimum Value = 0.5 W = 1.500267 1.47758434 1.522949616
Mean = 0.9
Wq = 0.0189379 0.014214235 0.023661518
Service Times
P0 = 0.0759385 0.068988925 0.082888121
Distribution = Erlang
P1 = 0.3678422 0.35533123 0.380353149
Mean = 1.5
P2 = 0.4001255 0.389988281 0.410262808
k = 4
P3 = 0.1364975 0.127031262 0.145963775
P4 = 0.0184091 0.014574934 0.022243189
Length of Simulation Run
P5 = 0.0010505 0.000226165 0.001874863
Number of Arrivals = 5,000
P6 = 0.0001366 -0.000130284 0.000403582
P7 =0 0 0
P8 = 0 0 0
P9 = 0 0 0
95% Confidence Interval