After you determine the activity durations, you have a range associated to the it (duration +/- sigma). If you now want to determine the critical path in the network diagram what figure should you use for each activity: duration or duration + sigma?
if the distribution of duration values is symmetrical (+- sigma), then the expected value will be the actual estimate without this variance, so you can use it simply for critical path estimation.
if distribution is assymmetric (for example a three-point estimation), you can use the E = (a+4m+b)/6 formula to get most probable duration value, and use this to determine critical path.
or, you can always use monte-carlo analysis if you have access to simulation software.
Estimates are probabilistic. The deterministic planning value you choose within that estimate range represents the degree of risk you wish to assume. You can create rules like using a PERT formula, or nothing less than the 60th or 70th percentile of the range, or Mean plus Sigma, or whatever else. But that limits your risk analysis and mitigation techniques.
For example: it takes you between 30 minutes to one and half hours to drive to the airport. Most times it takes about 50 minutes. If you are picking up your boss whom you do not like, you may choose to be very optimistic in your travel time, like 45 minutes, leaving quite a probability that he will be waiting for you at the curb. If you are picking up a valued customer, you may choose to be more pessimistic and leave a good hour to hour and fifteen minutes ahead so that there is more of a chance you will be waiting at the curb.
No formula can do that risk analysis for you.