Confidence with Estimating True Mean

[Physics_wiz]

Say I have a Gaussian random number generator that generates random numbers with an unknown mean x. I get a few random numbers from the generator and I want to estimate x. The estimate will, of course, be the average of the numbers (y), but how confident can I be that x is within a value, a, of y?

[EnumaElish]

You need to calculate the standard deviation of the sample and calculate the t-statistic:

http://en.wikipedia.org/wiki/Student%27s_t-test#Independent_One-Sample_t-test

then compare it against critical values in a probability table for Student's t distribution (http://en.wikipedia.org/wiki/T_distribution).