## terça-feira, setembro 05, 2006

### PMP Question - Probability that a process will finish in less than x days

( Wolfgang, I think you should read from scratch the chapter on Time Management of the PMBoK and the same chapter of the book "Das PMP-Examen" ).

Question :

"A process has Critical path of 12 days & Standard Deviation of 1. What is the probability that the process will be completed in 13 days.
A : 10%
B : 68%
C : 84%
D : 95%"

Answer: C ! I bet you would have chosen B. Wrong !! ( As the target date is 1 SD away, one might think that the right answer would be 68% ...).

The probability of PERT estimates is 50% and it is the mean.
1 SD from the mean covers an additional population of 34.1%, 2 SD from the mean covers 47.7% and 3 SD covers 49.8%. Conversely, -1 SD from the mean covers a population of -34.1% etc.
13 days means - 1 additional day from the mean (that is 1 SD too); so from the data above the cumulative probability to complete, comes from 50% + 34.1% = 84.1% (answer C).

To better understand my affirmation, we should consider a PERT estimate as a mean of a normal distribution (although PERT is based on a beta distribution but we all know that all the distribution can be approximated by a normal distribution), thus the area under the Gaussian curve delimited by the mean is 50% of the entire area.

As with many PMP math questions, one has to read between the lines, to perceive what is really being asked.