Analysis of a PERT problem shows the estimated time for the critical path to be 108 days with a variance of 64. There is a .80 probability that the project will be completed before approximately day:
A) 98
B) 108
C) 109
D) 115
E) 118

Question

Quizplus · Accepted Answer

To find the day by which there is an 80% probability of completion, we use the formula for the Z score in project management: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the target completion time, $\mu$ is the mean (108 days in this case), and $\sigma$ is the standard deviation (the square root of the variance, which is $\sqrt{64} = 8$). Looking up a Z score for an 80% probability in a standard normal distribution table gives us a Z score of approximately 0.84. Plugging the values into the formula gives us $0.84 = \frac{X - 108}{8}$. Solving for $X$ gives us $X = 108 + 0.84(8) = 108 + 6.72 = 114.72$, which rounds to approximately 115 days.

Analysis of a PERT Problem Shows the Estimated Time for the Critical