A project being analyzed by PERT has 50 activities, 12 of which are on the critical path. If the estimated time along the critical path is 176 days with a project variance of 144, the probability that the project will take 194 days or more to complete is
A) near zero.
B) 0.0126.
C) 0.0668.
D) 0.9332.
E) 2.00.

Question

Quizplus · Accepted Answer

To calculate the probability that the project will take 194 days or more to complete, we need to find the Z score first:
Z = (194 - 176) / √144 = 1.3333
Then, using a standard normal table or calculator, we can find the probability:
P(Z ≥ 1.3333) = 0.0918
However, we need to consider that the critical path has 12 activities, which means that the estimated time along the critical path follows a normal distribution with mean 176 days and variance (144/12) = 12 days squared. Therefore, we need to adjust the Z score and probability accordingly:
Z' = (194 - 176) / √12 = 3.055
P(Z' ≥ 3.055) = 0.0017
This is the probability that any one activity on the critical path will take longer than expected, assuming normality. However, since there are 12 activities on the critical path, we need to use the binomial distribution to calculate the probability that at least one activity will take longer than expected:
P(at least one critical activity takes ≥ 18 more days) = 1 - P(no critical activity takes ≥ 18 more days)
= 1 - (0.9983)^12
= 0.0668
Therefore, the probability that the project will take 194 days or more to complete is 0.0668, which is answer choice C.

A Project Being Analyzed by PERT Has 50 Activities, 12