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Quiz 5 Simulation 1.) The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution: Time Between Arrivals (min.) Probability 1 0.25 2 0.3 3 0.35 4 0.1 a.) Simulate the arrival of cars at the service station for 20 arrivals and compute the average time between arrivals. b.) Simulate the arrival of cars at the service station for 1 hour, using different stream of random numbers from those used in (a) and compute the average time between arrivals. c.) Compare the results obtained in (a) and (b) to the expected value. 2.) The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week is as follows: Machine Breakdowns per week Probability 0 0.05 1 0.15 2 0.2 3 0.3 4 0.25 5 0.05 a.) Simulate the machine breakdowns per week for 20 weeks. b.) Compute the average number of machines that will break down per week and compare to the expected value. 3.) Simulate the following decision situation for 20 weeks and recommend the best decision. A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manage estimates that the following profits will result from each decision given each set of weather conditions: Decision Weather Rain Overcast Sunshine .30 .15 .55 Sun Visors \$-500 \$-200 \$1,500 Umbrellas 2,000 0 -900 4.) Every time a machine breaks down at the Dynaco Manufacturing Company (problem 2), either 1, 2, or 3 hours are required to fix it, according to the following probability distribution: Repair Time (hr.) Probability 1 0.25 2 0.55 3 0.20 a.) Simulate the repair time for 20 weeks b.) Compute the simulated average weekly repair time and compare to the expected value.
Answered 2 days AfterNov 18, 2022

## Answer To: Quiz 5 Simulation1.) The time between arrivals of cars at the Petroco Service Station is defined...

Baljit answered on Nov 21 2022
Quiz 5 Simulation
1.)
Probability distribution range for Time between Arrivals
Time Between Arrivals (min.)
Probability
Cumulati
ve Probability
Random Number Range, r1
1
0.25
0.25
0-24
2
0.3
0.55
25-54
3
0.35
0.9
55-89
4
0.1
1
90-99
a. Simulation of the arrival of cars at the service station for 20 arrivals
Tabular Simulation
Trials
Random number
Time Between Arrivals (min.)
1
4
1
2
35
2
3
6
1
4
93
4
5
30
2
6
78
3
7
19
1
8
88
3
9
70
3
10
84
3
11
91
4
12
80
3
13
18
1
14
55
3
15
3
1
16
6
1
17
52
2
18
77
3
19
29
2
20
69
3
SUM

46
The Average Time between Arrivals=46/20=2.3 Minute/car
b.
c.
Expected Value of Average time between arrival=(1*0.25+2*0.3+3*0.35+4*0.1)=2.3 minute per car which is as same as from our simulation result.
2.)
Probability distribution range for Machine breakdown
Machine Breakdowns per week
Probability
Cumulative
probability
Random number range
0
0.05
0.05
0-4
1
0.15
0.2
5-19
2
0.2
0.4
20-39
3
0.3
0.7
40-69
4
0.25
0.95
70-94
5
0.05
1
95-99
a.) Simulation of the machine breakdowns per week for 20 weeks
Tabular Simulation
Weeks
Rn1
Machine 1 Breakdown
Rn2
Machine 2 Breakdown
Rn3
Machine 3 Breakdown
Rn4
Machine 4 Breakdown
Rn5
Machine 5...
SOLUTION.PDF