GATE ME 2021 Set 1 — Question 45
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Engineering Mathematics → Operations Research → Normal Distribution
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Question
Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.
The probability that the project will be completed within 40 days is ______ (round off to two decimal places).
(Note: Probability is a number between 0 and 1).
| Activity | A | B | C | D |
|---|---|---|---|---|
| Mean (days) | 6 | 11 | 8 | 15 |
| Variance (days) | 4 | 9 | 4 | 9 |
(Note: Probability is a number between 0 and 1).
Correct answer
0.5 to 0.5
Solution
1.The mean duration of the project () is the sum of the means of the activities on the critical path:
days.2.The variance of the project duration () is the sum of the variances of the activities on the critical path (since they are independent):
days.3.The standard deviation is days.
4.We need to find the probability .
5.Calculate the standard normal variable :
6.For , the area under the standard normal curve to the left is .
Therefore, the probability is 0.50.Continue learning with Success Tracker
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