Empirical Rule. Is it applicable/usable in this case? So I ran in this problem: I have to test whether Empirical Rule is applicable. Proportions I got is 73%, 94,7% and 99.1% (within one, two and three standard deviations). I'm worried about 73%. This is quite far away from 68% (that the empirical rule states). I have more than 1500 random variables. Can I still state that Empirical Rule works here? What are the acceptable deviations?
 A: The "empirical rule" (a term I dislike, because it's neither empirical, nor of much practical use as a rule) applies when the data are from a normal population, and even then only when the parameters are known*, and even then only on average.
* or from large enough samples to be very accurately estimated
So 
(i) you don't know that the sample is from a normal distribution. Data are often not so close normal. Why should a rule for normal distributions hold? The two-standard-deviation part of the rule often isn't too far out with unimodal distributions - but can often be a good deal further away than you got.
(ii) you estimated the mean and standard deviation, and even if you had the original data from a normal distribution, the appropriate rule when you have the mean and standard deviation estimated from the data will be based on a t-distribution (with really large samples like yours this won't be much of an issue though)
(iii) since sample proportions can vary from their population values, even when the true population proportions within 1, 2, and 3 population standard deviations of the population mean are as the rule states, the observed proportions will differ from them. Under independence, they'll be binomially distributed (scaled binomial). So we expect some variation from the rule.
For a sample size of 1500 from a normal distribution with known population mean and sd, you'd expect
                 Expected        95%ish interval 
                 proportion      for sample
                 in range        proportion(%)
within 1 sd       68.27%         65.93-70.60
within 2 sd       95.45%         94.40-96.47
within 3 sd       99.73%         99.40-99.94

(These intervals are based on binomial calculation; normal intervals may differ slightly.)
As you see, the first and last seem a bit outside those ranges, so might be somewhat surprising to see your results if the data really were normal ... but again, why should it be normal? If it isn't, why should it follow that rule?
