Question

A project's critical path is ABDE. The project activity information (in weeks) are as follows. Assume the project finish time follows a normal distribution.

Activity A B C D E F
Expected FT 8 7 5 6 3 4
Variance 4 5 2 6 2 2

If the project deadline is set to be 26 weeks, then what is the z-value to determine the probability that the project will be finished before the given deadline?

Answer 1

To find the z-value for the project completion probability, calculate the sum of the expected times for critical path activities (24 weeks) and their variances (17), and then calculate the z-score using the deadline (26 weeks), mean duration, and standard deviation (4.1231 weeks) to get a z-value of approximately 0.485.

Step-by-step explanation:

To calculate the z-value for the probability that the project will be finished before the 26-week deadline, you need to first determine the mean project duration and the standard deviation of the project completion time based on the critical path activities. The mean project duration (expected finish time, FT) is the sum of the expected times for activities on the critical path, which are A, B, D, and E. So, the mean project duration is 8 + 7 + 6 + 3 = 24 weeks. The variance of the project completion time is the sum of the variances of the activities on the critical path. Using the provided variances for activities A (4), B (5), D (6), and E (2), the total variance along the critical path is 4 + 5 + 6 + 2 = 17. The standard deviation is the square root of this variance, which is approximately 4.1231 weeks.

Now, the z-score is calculated using the formula: z = (X - μ) / σ, where X is the deadline (26 weeks), μ is the mean project duration (24 weeks), and σ is the standard deviation (4.1231 weeks). Plugging the numbers in yields z = (26 - 24) / 4.1231, which gives us a z-value of approximately 0.485.

Therefore, the z-score for determining the probability that the project will be finished before the 26-week deadline is approximately 0.485.