A project whose critical path has an estimated time of 120 days with a variance of 100 has a 20% chance that the project will be completed before which day (rounded to nearest day)?
A) 98
B) 112
C) 120
D) 124
E) 220

Question

Quizplus · Accepted Answer

First, we need to calculate the standard deviation of the critical path:

SD = sqrt(variance) = sqrt(100) = 10

Then, we can use the normal distribution to find the z-score that corresponds to a 20% chance of completing the project before a certain day:

P(X < x) = 0.2

z = (x - mean) / SD

z = (x - 120) / 10

Looking up z = -0.84 in a standard normal distribution table, we find that the corresponding value of x is:

x = (z * SD) + mean = (-0.84 * 10) + 120 = 112

Therefore, the project has a 20% chance of being completed before day 112, so the answer is B.

A Project Whose Critical Path Has an Estimated Time of 120