GATE 2021 ME (ME1) – Question 45
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.
| Activity | A | B | C | D |
|---|---|---|---|---|
| Mean (days) | 6 | 11 | 8 | 15 |
| Variance (days²) | 4 | 9 | 4 | 9 |
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).
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Show answer and explanation
Correct answer: 0.49 to 0.51
Explanation
The sum is normal with mean 6+11+8+15=40 days and variance 4+9+4+9=26 days².
The requested deadline equals the mean. Normal symmetry gives $P(T\le40)=\Phi(0)=\mathbf{0.50}$.