Free PMP Certification Practice Questions:


You have been recently been assigned to provide an accurate project schedule for a large construction project. You are evaluating the network diagram for the construction project.

Using Three Point Estimating techniques, your lead engineer has given you the following completion estimates for several critical path activites, assuming a beta distribution model. Based on the table below, which of the following statements are true?





A) There is approx. a 50 percent chance that the project will complete between 64 days and 78 days

B) There is approx. a 95 percent chance that the project will complete between 64 days and 78 days

C) There is approx. a 99 percent chance that the project will complete between 64 days and 78 days

D) There is approx. a 95 percent chance that the project will complete between 57 days and 85 days


  • [Ans: D]


    • Three-Point Estimating is a technique for estimating and planning large projects. One of its advantages is the ability to manage probabilities associated with the project. Three-Point Estimating utilizies simple statistical mathematics in order to construct a probability distribution for the completion dates of the project milestones.



    Without getting too involved in the statistics and mathematics, a project will have a 68.26 percent chance of being completed within one standard deviation from the mean. The project will have a 95.44 percent chance of being completed within two standard deviation from the mean. And the project will have a 99.73 percent chance of being completed within three standard deviation from the mean.



    Specifically, to calculate the the probability distribution for the completion dates of the project, one needs to calculate the expected value / mean and standard deviation for the entire project.



    The expected value / mean of the project is simply the sum of the individual expected values for each of the activities.


    Task A (EV)- 10.50 days

    Task B (EV) - 41.50 days

    Task C (EV) - 19.17 days

    Total Expected Project Duration = 71.17 days



    The standard deviation for the project can be calculated by calculating the standard deviation of each activity, adding up the squares of each activity's standard deviation, and then taking the square root of this sum.


    Task A (SD Squared) = 4.69

    Task B(SD Squared) = 30.25

    Task C(SD Squared) = 14.69

    Total (SD Squared) = 49.64

    Standard Deviation Of Project = SquareRoot (Total [SD Squared]) = SquareRoot (49.64) = 7.04



    Hence, there is a 68.26 percent that the project will complete in one standard deviation from the mean, which is between 64.13 days (71.17-7.04) and 78.21 days (71.17 + 7.04)



    There is a 95.44 percent that the project will complete in two standard deviations from the mean, which is between 57.09 days (71.17 - (2*7.04)) and 85.25 days (71.17 + (2*7.04))



    There is a 99.73 percent that the project will complete in three standard deviations from the mean, which is between 50.05 days (71.17 - (3*7.04)) and 92.29 days (71.17 + (3*7.04))





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