A PERT project has 45 activities, 19 of which are on the critical path. The estimated time for the critical path is 120 days. The sum of all activity variances is 64, while the sum of variances along the critical path is 36. The probability that the project can be completed between days 108 and 120 is
A) -2.00
B) 0.0227
C) 0.1058
D) 0.4773
E) 0.9773

Question

Quizplus · Accepted Answer

First, we need to find the standard deviation of the critical path, which is the square root of the sum of variances along the critical path (36): 
sqrt(36) = 6

Next, we need to find the z-score for the range of days in question (108 to 120):
z = (x - μ) / σ, where x is the upper limit of the range (120), μ is the mean (120), and σ is the standard deviation (6).
z = (120 - 120) / 6 = 0

Using a standard normal distribution table or calculator, we can find the probability of a z-score of 0: 
P(z = 0) = 0.5

Therefore, the probability that the project can be completed between days 108 and 120 is 0.5, or 50%. Converted to a decimal, this is 0.5.

The correct answer is D (0.4773), which is the closest option to 0.5.

A PERT Project Has 45 Activities, 19 of Which Are