In a normally distributed population that is very large, mu was found to be 100 and sigma = 20. If a sampling distribution of the sample mean was constructed with 36 observations in each sample, what would be the standard deviation of that sampling distribution? Between what two values would the middle 95% of the sample mean fall?

I've tried several different formulas to figure these out but it seems I'm doing circular sort of computations. How can you find the standard deviation of a sample distribution when you know the population information?

Any suggestions would be great, it probably is something simple I'm overlooking.

Jon