I have a dataset originated from a practical setting, but it is not clear to me how to interpret it. Let me try to frame the setting and see if it makes sense:
A manufacturer produces a type of product that use noise level (dB) as one of its quality metrics. All products during a production cycle are expected to have similar or consistent noise levels. Further, Let's say this "consistency requirement" is defined here as "the max and min noise level should not differ more than $x$ percentage point from the mean".
My question are two-fold:
Is it possible to use some distribution metrics, for example, standard devision, to make claim such as: if the $sd < a$, then it will meet the consistency requirement?
It seems intuitively that the more products produced in the cycle, the harder it is to meet the consistency requirement. Statistically, each product's noise is independent variable, the larger the population, the larger the variation of sum - is this a correct understanding/statement?