You need to calculate variances of all 4 cases and then take sqr root of that to get the std variance.

I hope this would help

Rebecca,

the formula is that the path standard deviation is the square root of the summed up squares of the single SDs. 

A single SD (= sigma) is defined as a 6th (±3 Sigmas) of Pess. minus Opt.

Single SDs are: Act. A: 2 days, Act. B: 1 day;  Act. C: 2 days, Act D: 3 days, Act. E: 3 days.

SD squares are therefore:  Act. A: 4; Act. B: 1;  Act. C: 4; Act D: 9; Act. E: 9 

SD squares, sum: 27

Square root of that: 5.19 days

This means that the distance between a pessimistic and an optimistic estimate for the entire path duration should be 6 x 5.2 = 31.2 days.

It is one of my toughest questions, and I hope that you won't see it in the exam, but who knows for sure?

 I have explained and detailed these kinds of question in my thread at pmptrend.com forum with graphs u can visit that thread

For complete explanation on PERT and SD, you can read following articles
* PERT Formula and Use of Standard Deviation - http://www.pmbypm.com/pert-and-standard-deviation/
* How to use PERT, CPM and Standard Deviation Together? - http://www.pmbypm.com/critical-path-pert-and-standard-deviation/