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Cheers for the good work around here

My question is probably quite basic: how do we proceed - theoretically and by experience/practice - to say that the measurements of such characteristic should follow such distribution?

I am particularly interested to know the generic procedure (the actual analysis idea), and would like to see it applied to the case of the normal distribution...

As a background, our customer gave us a table with a list of different characteristics (basically dimensional and geometrical tolerances) and the corresponding distributions expected. Apart from the question whether the table is correct or not and that we could eventually discuss some specific cases if we have solid understanding of our process, I am wondering on which basis such a table was made?

I know that theoretically the central limit theorem is used to expect the normality of some data, but I don't have enough experience to understand its application on specific cases... Example: why would the data from a dimensional tolerance with two specification limits follow a normal distribution (question from the CLT point of view)? What are the independent random variables we're considering in this case?

Many thanks in advance