1. The distribution of the offset will depend on the function on which the offset is computed. You can refer to the wikipedia article on "Normal Distribution" under the section titled "Related distributions".
2. Normally, we run MC to guarantee a certain yield in production. One way of specifying yield is in percentage terms, ie we want 99% of offsets to fall within specifications. Another way is to specify in sigma count, ie a 3-sigma design translates to a 99.87% yield for a parameter distribution assumed to be Gaussian.
3. As MC simulations creates a sample population, any mean or std computed from this sample population are merely estimates of the actual statistical parameters, with a more accurate estimate requiring a larger population (Refer to any statistical texts).
In other words, you seriously don't expect to be able to obtain accurate estimates of meeting a 3-sigma yield based on only 30 samples. Try 1000 instead.