# PERT formula question - Need help

Together with your team, you applied three-point estimation on a critical path with constist of two activites.

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 formual for the paths, what is the duration uncertainty of the entire path?

A. 21 days

B. 30 days

C. 42 days

D. No statement is possible from the information given.

### Here it's given that:Duration

Here it's given that:

Duration uncertainty(DU) = Pessimistic est.(P) - Optimistic est.(O); DU1 = 18 and DU2 = 24;

[and we know σ(standard deviation) = (P - O) / 6, so we can also say that σ = DU / 6 ------ (A)]

So for first activity, σ1 = 18 / 6 = 3{using (A)}; variance1 = 3^2 = 9;

Similarly, σ2 = 24 / 6 = 4; variance2 = 4^2 = 16;

Now, since these two activities are on the critical path, their variances can be added. So path variance = variance1 + variance2 = 9 + 16 = 25;

and σ of the entire path = sq. rt.(path variance) = sq. rt. (25) = 5

Again using (A), DU of the entire path = σ(path) * 6 = 5*6 = 30

So correct option is B.

Am I correct jcrajput?

### it could be understood like that

In 1st Activity

Suppose Pess duration is = X days

Difference is 18 days , hence  opt duration will be  = X -18 days

In second actvity

Suppose Pess dur  = Y days

Diff = 24 days , hence opt du = Y-24 days

X+Y will be pess dur for  both activities

where as Opt dur will be  = (X-18 +Y-24) days

Now Total uncertainity diff of combined package = P-O = X+Y - (X-18 + Y -24)

=  42 days

### What's the correct option

What's the correct option Rajput?

### The correct answer is B. That

The correct answer is B. That is 30 days.

This is question # 94 from Oliver F. Lehmann 175 questions.

Thank you for explanation.

### WOW!!!!

Great Diba. Good explanation as well. If I could understand it, anyone else will. All the best Man!!! Enjoy! KK....

### Here is another way to solve

Here is another way to solve it:

Standard Deviation (pessimistic minus optimistic estimate) is given for 2 activities

Activity 1 Standard Deviation = 18 days

Activity 2 Standard Deviation = 24 days

Variance for Activity 1 = 18x18 = 324

Variance for Activity 2 = 24x24 = 576

Total Variance on critical path = 324+576 = 900

SD for the entire path = Square Root of 900

SD for the entire path = 30 days

### Ameen,Standard deviation

Ameen,

Standard deviation isn't = (pessimistic est. - optimistic est.) .. it's rather = (pessimistic est. - optimistic est.)/6 ..

I would say that your solution is arithmetically correct(since you've ignored the division by 6 all throughout, the answer is correct) but technically incorrect.

### Diba, your method to solve

Diba, your method to solve this question is absolutely correct; however, both methods give you exactly the same answer with any combination you use. Thanks for the correction :)

### thanks everybody

Thanks to correct me

only the correction in Diba solution is 18 and 24 and 30 is not Du but Diff.

This question is based on or like of q 27 of O L 75 q.

Regards