There are 4 paths as follows: Path 1: Start → 1 → 4 → 5 → 6 → 7 → 8 → 9 → 10 → End Path 2: Start → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 → 10 → End Path 3: Start → 1 → 4 → 5 → 6 → 7 → 8 → 11 → End Path 4: Start → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 11 → End What are the mean and the variance of the duration of each path? What is the longest path in mean time? Fill in the following table and identify the longest path in mean time. Mean Variance Path 1 Path 2 Path 3 Path 4
There are 4 paths as follows:
Path 1: Start → 1 → 4 → 5 → 6 → 7 → 8 → 9 → 10 → End
Path 2: Start → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 → 10 → End
Path 3: Start → 1 → 4 → 5 → 6 → 7 → 8 → 11 → End
Path 4: Start → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 11 → End
What are the mean and the variance of the duration of each path? What is the longest path in mean time? Fill in the following table and identify the longest path in mean time.
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Mean |
Variance |
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Path 1 |
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Path 2 |
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Path 3 |
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Path 4 |
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Answer: The longest path in mean time is .
What is the probability of completing the longest path within 185 minutes? Assume that the duration of the longest path is normally distributed.
What is the time T for which the probability to complete the longest path is 95%? Assume that the duration of the longest path is normally distributed.
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SOLUTION:-
1.1
Activity/event a c b Mean Variance
Start
1 5 15 30 16.6666667 158.333333
2 5 15 25 15 100
3 10 20 30 20 100
4 5 10 15 10 25
5 10 20 40 23.3333333 233.333333
6 10 15 30 18.3333333 108.333333
7 10 30 40 26.6666667 233.333333
8 15 40 55 36.6666667 408.333333
9 5 10 30 15 175
10 3 7 10 6.66666667 12.3333333
11 15 20 40 25 175
End
1.2
Variance
Mean
Path 1 169.25 16381.1667
Path 2 19.0740741 15291.4383
Path 3 22.3809524 14421.2963
Path 4 172.916667 14201.3889
Answer: The longest path in mean time is Path 4.
1.3
z = (185 - 172.916667)/\sqrt{}14201.3889 = 0.10
The probability is 0.5404.
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