What are the assumptions for the Empirical Rule(69, 95, and 99.7)? I am a little confused about what  assumptions are needed to meet the Empirical Rule in statistics. Does the population need to follow the normal distribution or the sample need to follow the normal distribution?
As far as I know, the ER is only applied to a normal distribution and if the sample follows a normal distribution then the population must follow a normal distribution. So assuming a sample follows a normal distribution also guarantees that the population it came from also follows a normal distribution. So, the assumption, the sample follows a normal distribution, is enough to say the population follows a normal distribution. If we say the population follows a normal distribution then the sample also follows a normal distribution. So the ER can be also applied with the assumption stating "the sample follows a normal distribution."
I am just trying to show my understanding about my question. If I am not correct, please correct me.
 A: The empirical rule applies when the observations appear to be drawn from a population that is normal. That population could be standard normal or $N(-57632, 838074)$. It’s just the normality that matters.
A: I think the whole point is that it is an empirical rule, which often applies in practice (except that it is an approximation, and except when it doesn't).
The rationale for the empirical rule is just that many distributions resemble the normal or Gaussian in this respect. There is no theorem behind this, and it's easy to find exceptions.
The expression says as much about English usage as it does about statistics. The word rule is overloaded, and there are several meanings. Here are some:

*

*Identifying a procedure that must be followed, as say rules in elementary algebra for handling expressions given elements, operators, parentheses and the like, or rules in chess on how pieces may move, take each other, and so on. A rule of this kind requires understanding, but leaves no scope for discussion, except that if you want chess or an algebra with different rules, it's a different game. Sometimes a rule of this kind could be called a law.


*A law or regulation in some sense implying penalties if broken and apprehended, say to do with money handling or forbidden actions (being offside, swearing at an umpire or referee) in some sport.


*A rule (in British English, and perhaps in other dialects too, often "a rule of thumb") which is an approximation to what happens in nature or society. These run the spectrum from serious to facetious, as in a conifer growing 1 foot yearly, or 10 cm of fresh snow being the equivalent of 1 cm of rain, or 20% of the people doing 80% of the work.
The rule here is closest to sense #3.
