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 less to complete is

A) near zero.
B) 0.0126.
C) 0.0668.
D) 0.9332.
E) 2.00.

To find the probability that the project will take 194 days or less to complete, we use the formula for the Z score in PERT: $Z=\frac{X-\mu }{\sigma }$ , where $X$ is the desired time (194 days), $\mu$ is the mean time along the critical path (176 days), and $\sigma$ is the standard deviation ( $\sqrt{144}$ = 12 days). Plugging in the values, we get $Z=\frac{194-176}{12}=\frac{18}{12}=1.5$ . Looking up the Z score of 1.5 in the standard normal distribution table gives a probability of approximately 0.9332, indicating the project has a 93.32% chance of being completed in 194 days or less.