VENDINGMACH?NEREPA?RSÍMA IV) 20 PTS COMPLAINTSARE RECEIVED PERIODICALLY ABOUT TH
ID: 422449 • Letter: V
Question
VENDINGMACH?NEREPA?RSÍMA IV) 20 PTS COMPLAINTSARE RECEIVED PERIODICALLY ABOUT THE VENDING MACHINES ON CAMPUS WITH REGARD TO THEIR OPERATION, THE NUMBER OF VENDING MACHINE COMPLAINTS RECEIVED WEEKLY HAVE BEEN RECORDED THE NUMBER OF COMPLAINTS RECEIVED WEEKLY HAVE BEEN RECORDED AND ARE DISPLAYED BELOW: NO. VENDING MACHINE PERCENTAGE OF COMPLAINTS WEEKLY WEEKS 0.30 0.10 0.10 0.10 0.40 1) 8 PTs. CONDUCT A SIMULATION OF WEEKLY COMPLAINTS REGARDING VENDING MACHINE OPERATION, CONDUCT YOUR SIMULATION FO 20 E USING THE RANDOM NUMBERS SHOWN BELOW. NOTE THAT THESE NUM- BERS HAVE BEEN OBTAINED FROM A TWO DIGIT RANDOM NUMBER TABLE. MAKE SURE TO SHOW THE RANDOM NUMBER RANGES YOU ASSIGNED. 27, 85, 93, 74, 15, 55, 22, 37, 48, 77, 04, 88, 23, 12, 67, 97, 54, 08, 31, 44 4 PTS. 2) FROM YOUR SIMULATED RESULTS, CALCULATE THE AVERAGE NUMBER OF WEEKLYCOMPLAINTS REGARDING VENDING MACHINES. SHOW YOUR CALCULATION. . 4 PTS. 3) CALCULATE THE LONG-RUN EXPECTED NUMBER OF WEEKLY COMPLAINTS REGARDING VENDING MACHINES FROM THE ORIGINAL DISTRIBUTION OF COMPLAINTS GIVEN. (HINT: YOU DON' T NEED THE SIMULATION RESULTS TO CALCULATE THIS VALUE!!!) SHOW YOUR CALCULATION!!! 4 PTS. 4) IN A FEW WORDS, EXPLAIN ANY DIFFERENCE BETWEEN THE AVERAGE AND EXPECTED VALUES FOR COMPLAINTS. (GIVE THIS EXPLAN- ATION EVEN IF THE RESULTS YOU OBTAINED WERE THE SAME BY CHANCE.) Page 1Explanation / Answer
Monte Carlo Simulation:
1. In the simulation model, set-up probability distribution for the variables to be analyzed.
2. Build cumulative probability distribution for each random variable.
3. Generate random numbers and then, assign an appropriate set of random numbers (RN) to represent a value or range (RN interval) of values for each random variable. Normally, random numbers 0.0—.99 (100 in count) are assigned to variables.
4. Conduct the simulation experiment using random sampling or according to the given sets of random numbers.
The probability of zero complaints is 0.30, assign 30 random numbers, 00 to 29 (but less than 30) to get zero complaints. Similarly, the probability for one complaint per week is 0.1, the next ten numbers from 30 to 0.39 would be assigned to this level. Similarly other RN intervals are identified as follows
No. of complaints per week
Probability
Cumulative Probability
Random Number Intervals
0
0.30
0.30
(00 to 29)
0 but less than 30
1
0.10
0.40
(30 to 39)
30 but less than 40
2
0.10
0.50
(40 to 49)
40 but less than 50
3
0.10
0.60
(50 to 59)
50 but less than 60
4
0.40
1.00
(60 to 99)
60 but less than 99
Simulation Trials
Random Number
Simulated Payment
1
27
0
2
85
4
3
93
4
4
74
4
5
15
0
6
55
3
7
22
0
8
37
1
9
48
2
10
77
4
11
04
0
12
88
4
13
23
0
14
12
0
15
67
4
16
97
4
17
54
3
18
08
0
19
31
1
20
44
2
Total no. of complaints in 20 days
40
Average number of complaints = Total no. of complaints/No. of run days = 40/20 = 4
Average number of weekly complaints regarding vending machine = 4 complaints per week.
Part 3)
Expected no. of weekly complaints = sum of product of no. of complaints and respective probabilities
Expected no. of weekly complaints = (0 x 0.30) + (1 x 0.10) + (2 x 0.10) + (3 x 0.10) + (4 x 0.40) = 2.2
Long-term Expected no. of weekly complaints = 2.2 complaints per week
No. of complaints per week
Probability
Cumulative Probability
Random Number Intervals
0
0.30
0.30
(00 to 29)
0 but less than 30
1
0.10
0.40
(30 to 39)
30 but less than 40
2
0.10
0.50
(40 to 49)
40 but less than 50
3
0.10
0.60
(50 to 59)
50 but less than 60
4
0.40
1.00
(60 to 99)
60 but less than 99
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