Standard Deviation

Can somebody explain the following question please?

A project manager has been asked by the client to meet the promise date of the project. The project manager analyzes the schedule before promising a date to the customer. The project manager uses the program evaluation and review technique to evaluate the project schedule. She decides that based on the PERT calculations she can promise a delivery date of June 30. The expected value of the project completion date is May 30. If the project manager is willing to accept a 5% probability that the project will be delivered later than June 30, what is the standard deviation of the duration of the activities on the critical path? Assume a five-day workweek.

a. Ten days
b. Fifteen days
c. One-half month
d. One month


As per 3point estimate (PERT - wieghted average beta distribution method)

ans will be 15 days

refer earlier Question

Thanks a lot.





5.2. Probability of Project Completion by Due Date

Now, although the project is estimated to be completed within 28 weeks (te=28) our Project Director would like to know what is the probability that the project might be completed within 25 weeks (i.e. Due Date or D=25).

For this calculation, we use the formula for calculating Z, the number of standard deviations that D is away from te.

By looking at the following extract from a standard normal table, we see that the probability associated with a Z of -0.6 is 0.274. This means that the chance of the project being completed within 25 weeks, instead of the expected 28 weeks is about 2 out of 7. Not very encouraging.



On the other hand, the probability that the project will be completed within 33 weeks is calculated as follows:

The probability associated with Z= +1 is 0.84134. This is a strong probability, and indicates that the odds are 16 to 3 that the project will be completed by the due date.



If the probability of an event is p, the odds for its occurrence are a to b, where:

Select Bibliography

Wiest, Jerome D., and Levy, Ferdinand K., A Management Guide to PERT/CPM, New Delhi: Prentice-Hall of India Private Limited, 1974

Render, Barry and Stair Jr., Ralph M. - Quantitative Analysis for Management, Massachusetts: Allyn & Bacon Inc., 1982, pp. 525-563

Freund, John E., Modern Elementary Statistics, New Delhi: Prentice-Hall of India Private Limited, 1979

Most of the places I saw that this question is wrongly answered as option C =45 days(one and half month), without any justification.

I saw a blog in PMHUB, and many other sites , all are just copying , as 45 days without knowing the reasons why.

Some of them are little adding it with 95 % probability (appx) of 2sigma and thus of normal distribution but still they are answering 1.50month.

If It is by 2sigma of NDC, then one sigma = 31/2= 15days appx, also answer comes B. But it is wrong approach.

at here 95 % is different then


shown in NDC figure

see 47.87 (LHS)+47.87(RHS) = 95.73 %

where as in question it is

50(LHS) + 45 (RHS) = 95%

it makes a great difference

47.87-45 = 2.87%

with this difference at ends (flattered curve) = 45will give 1.65SIGMA, (value of Z, in Z score curve), while 47.87 will give  = 2sigma.


It can be checked in Excel program also

There is one formula  NORMINV ( prob %age in decimal, MEAN DATE, SD) will give END date (pessimestic date).

But in this question given  M = a Mean date, Prob %age = 95% and End date and asking SD =?

Could not be solved , directly.

But by indirect , by GOAL seek function of Excel  =

Putting in formula NORMINV (0.95,30th May,SD) = 30th of June, by goal seek will give SD = 18.80 days( it also works on Normal Distribution Curve theory)


BY PERT  formula SD = P-O/6, Beta distribution , weighted average, method

Assuming -3sigma as Optimistic values = 3*31/1.645= 54 days, and pessimistic as cutoff date at 95% prob = 31 days from mean

= p-o/6 = 85/6  =14.1 appx = 15 days.


By no  other way answer will come.


The ans would be 15 days.

For complete explanation on PERT and SD, you can read following articles

* PERT Formula and Use of Standard Deviation

* How to use PERT, CPM and Standard Deviation Together?