the "simple" explanation

Statistical methods are all about the data, and in the mass production world there is plenty of it.  We prefer our statistical predictions be as accurate as scientifically possible, and quite frankly, the more data the greater that accuracy.  Is it possible to apply these methods to other businesses?  Of course, but the mass production world allows us to make - and test - our statistical inferences relatively easily and quickly.

the "statistical" explanation

It's all about the confidence intervals, which are used to statistically determine a level of certainty regarding the assumptions we make from sample data sets.  Let's first examine the CI for the mean:

The confidence interval for the mean is formed by an addition and subtraction - from the mean - of the sigma divided by the square root of the number of samples (or degrees of freedom).    Therefore the CI "shrinks" as the number of samples increases, such that the limit of the term added or subtracted approaches zero as the number of samples approaches infinity (an asymptotic relationship). 

The confidence interval for the sigma is considerably more complicated, as it is dependent upon the tails of the chi-squared distribution - the mean of the chi-squared equaling the number of samples (or degrees of freedom) and the variance (sigma squared) equaling twice the mean (or degrees of freedom).    Therefore the kurtosis is inversely proportional to the degrees of freedom, so the tails - used in the "range" of the CI - contain less area for greater DOF, in essence "shrinking" the CIs.  As with the CI for the mean, the limit of the term - this time multiplied by the calculated sigma - approaches zero as the number of samples approaches infinity (an asymptotic relationship).