Gaussian distribution in Astronomy

1. What does it mean for a data set to have gaussian distributed noise?
2. What does an error bar on a data point really imply?
3. What does a 5-sigma result mean? How often is a 5-sigma result wrong?
4. What does a 3-sigma upper limit mean?
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3. A 5 sigma result is a measurement that is that far from some background level. There may be a broad source of light that you can put a smooth curve through and a bright spot in the middle of it. The null hypothesis is that there is nothing there and the bright spot is a fluctuation in the noise. A 5 sigma result says the null hypotheses is ruled out to that level. If you believe the Gaussian model, it would only be wrong about one time in $10^{12}$. Experience says otherwise, however.