Quote:
Originally Posted by Relmiw
How much less than variance? What if the mean is 1000 and the variance is 300? 900? 990? Are you looking at a sample mean confidence interval?

Depends upon sample size. Suppose that there were 10^100 observations. the variance would be almost 0 regardless of the true model (assuming mean = 1000) This is the Law of Large Numbers.
There are two ways to answer your problem. One is practical, fit both models and then test which fits better.
Second, statistically test if you can reject the null hypothesis: mu = sigma.