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 day (rounded to nearest day).
A) 98
B) 112
C) 120
D) 124
E) 220

Question

Quizplus · Accepted Answer

The first step is to calculate the standard deviation (σ) of the critical path using the variance (VAR) given:

σ = √VAR = √100 = 10

Next, we can use the normal distribution to find the z-score associated with the 20th percentile (or 0.20 probability of completion before a certain day) by looking it up in a standard normal table or using a calculator.

For example, with a calculator: 
invNorm(0.20) = -0.84

The formula to calculate the day (d) associated with a certain z-score is:

d = μ + zσ

where μ is the expected completion time (120 days in this case), and z is the z-score we just found.

So,

d = 120 + (-0.84) * 10 = 112.4

Rounding to the nearest day gives:

Answer: B

A Project Whose Critical Path Has an Estimated Time of 120