TOPIC: Why is this the correct answer?

Hi,

I don't understand how this answer was calculated for the question from Oliver Lehmann's free 75 question test.
Can anyone please enlighten? The correct answer is B ie. approx. 5.2 days.

27. A project manager made 3-point estimates on a critical path and found the following results: (Check attached table below)

Assuming ±3 sigma precision level for each estimate, what is the standard deviation of the allover path?

(A) App. 4.2 days
( App. 5.2 days
(C) App. 6.2 days
(D) You can not derive the path standard deviation from the information given.

I am sure you have long since figured this out, but for those that have this question like I did. I have included one possible solution after playing around.

Variances are additive, and standard deviation is the square root of variance.

We can calculate the std of each activity, by subtracting the optimistic from the pessimistic.

That yields

[A,2]
[B,1]
[C,2]
[D,3]
[E,3]

Then add up the squares of the std deviations to get the total variance.

Total Variance = 27

Then take the square root to get 5.2