Profile Image for Rajesh K. Rajesh
  • Fri, Jul 23, 2010 5:20 PM


Together with your team, you applied three-point estimation on a Critical
path which consists of two activities. The following duration uncertainties
are all calculated assuming a ±3sigma Confidence interval. The duration
uncertainty-defined as pessimistic minus optimistic estimate-of the first
activity is 18 days; the second estimate has an uncertainty of 24 days.
Applying the PERT formula for paths, what is the duration uncertainty of
the entire path?


A 21

B 30

C 42

D No statement is possible from the information given

Replies to this Topic

21 is the answer.

I would say, the right answer is D. 

PERT formula requires at least three input parameters to calculate an estimated value: 

Estimated_Value = (Most_Optimistic_Value + 4*Average_Value + Most_Pessimistic_Value) ÷ 6

Even the formula is called three point estimate, it is in fact six point estimate (note the denominator). 

If we would have three or more experts provided with their estimates, giving us their thoughts on durations of each task, only in this case we would be able to apply PERT formula to came up with a three point estimate. 

With this, I think no statement is possible from the information given, so the answer is D. 

Best regards, 


Edited Thu, Aug 26, 2010 3:14 PM

Hi All,

This is a great resource for helping get familiar with questions for the exam. I have been reading for a week and plan to take the exam next month but I need to get the 35 contact hours completed. I would go for answer B on this question. I don't know about the PERT formulas but perhaps someone could clean up the answer into recognisable standard formulas. However, the question is about the value of sigma for the combined 2 activities. The first activity has a sigma of 3 days (18/6), the second activity has a sigma of 4 days (24/6), so combining them the overall sigma is 5 days (SQROOT (3squared + 4 squared)). Therefore 6 sigma of the combination is 30 days (ie 6*5days).



Profile Image for Pedro F. Pedro
  • Tue, Aug 31, 2010 4:52 PM

Well....this one is tough...I would say just adding the don't need the PERT formulas...if activity A has an uncertainty of 18, and B of 24...well, you just need to add them: 42, answer C

Anybody else?

One important detail is in the question. Read it: 

Applying the PERT formula for paths, what is the duration uncertainty of
the entire path?

So, making a statement such as you don't need the PERT formula is unacceptable, I think. 

It is a very good idea for the exam to learn how to answer the question. Read the question, and understand what is it actually asking, before making a decision to select the answer.  

Profile Image for Pedro F. Pedro
  • Tue, Aug 31, 2010 6:36 PM

Yeah, good point...but on the other hand, the is NO PERT formula for PATHS..the formula is for ACTIVITY duration only, not for the formula is not even applicable.

I read the question as having a problem with it, as probably did Pedro.

Idon't know what the PERT formula is for paths but if we are considering applying a formula that says (a +4y  +z)/6 then I would wonder why?

This question is merely asking you to sum the probability distribution functions of two activities when they are connected in series. In other words the 6 sigma range of one distribution is 18 days and the second 6 sigma range is 24 days. So the question is "what is the 6 sigma range of the combination".

The correct answer is 30 days as calculated in my response.

Pedero, you can't just add the sigma's because they are rms values.


Profile Image for abdullah M. abdullah
  • Tue, Aug 31, 2010 7:08 PM

first activity is 18 days so 18/6= 3

the second estimate has an uncertainty of 24 days  so 24/6=4

all calculated assuming a ±3sigma Confidence interval:

(3+4)=7 ====> 7* 3 sigma =21

so 21 is the answer

Hi Abdullah,

We are responding at the same time. I did wonder how the value 21 was derived. I think that answers A & D are provided because they are the 2 that can immediately be ruled out without any calculation. There is sufficient information to calculate the answer and the answer cannot possibly be a better estimate than the value 24 ( if you add uncertainty to the range 24 it will be a number bigger than 24).

Answer C is plausible but it is there to trick.


Profile Image for abdullah M. abdullah
  • Tue, Aug 31, 2010 7:54 PM

thank you Darek for your clarification

i think the answer it will be:

Sigma level is given here to misslead.

Formulas to be used in this calculation:

Standard Deviation (SD) = (P-O)/6

Variance = Square (SD)

Cumulative Variance = Variance of Activity1 + Variance of Activity2

Project Standard Deviation = Square Root (Cumulative Variance)





SD = (P-O)/6

Variance = SD*SD









Cumulative Variance




Project Standard Deviation = Square Root (Cumulative Variance) = 5

P-O = SD * 6 = 30 (Derived from the formula SD = (P-O)/6)

the answer is 30

agree with me ?

Edited Tue, Aug 31, 2010 8:10 PM

Profile Image for Pedro F. Pedro
  • Tue, Aug 31, 2010 8:30 PM

So far I think Abdullahs rational makes the most sense to me...but Derek isn't wrong either, and you're right, one can't simply add them...

People, don't kill yourself with so complicated theoretical researches. You will have no time for this during the exam. Read the question again, read about PERT formula in PMBOK.

The new PMBOK4 explicitly states the PERT formula in both Time and Cost Management chapters.

PERT stands for Program Evaluation and Review Technique. It is used to provide a more accurate estimate by considering the estimation uncertainty and risk.

PERT factor in best case (optimistic) and worst case (pessimistic) estimates.

The PERT formula is: (O+4M+P)/6 Where O is the optimistic estimate, P is the pessimistic estimate and M is the most likely estimate.

The formula is easy to remember and will probably come up in the PMP exam.

So learn it and pick up easy points for it in the PMP certification exam.

The answer to this question is definitely D. 

Good luck!

Abdullah, That's correct. The value sigma is a root mean square. That means you have to square each sigma, add them all together and then take te sq root to get the root mean square of the combination. The value 6 sigma = 30 days is a range - equivalent to O-P in the PERT Formula mentioned by Vitaliy. But we don't need PERT for this question because that would calculate a specific value for the duration (we can't do this because we don't know the Most Likely value). But the question only asked for the range (ie 6 * sigma).


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