I have a large dataset (e.g. 1000) concerning nuclear radiation measurements (if I call it Z) where each data point is related to a barrel. These barrels must later on be deposited in a large container. Because of some spatial restrictions, I can only use a part of these barrels (e.g. 700). So, each Z-value is assigned to one barrel. For my problem, I must choose these 700 barrels as such that the mean of Z is close to 1. For sure, there are more than 1 possible combinations (700 barrels) where the mean of Z = 1.
I need to establish a simulation method by which I can find all the possible combinations of barrels (700 out of 1000 vessels) where my criteria is full filled (mean Z =1). I need to register all these combinations for analyzing other properties later on.
My Z-values (1000 values) are not normally distributed. I assume that my dataset is not parametric. However, maybe that is not so relevant to the problem.
For these 700 barrels I need a random selection with replacement where I already know the outcome (mean of Z=1). So, I need to optimize my selection (700 out of 1000) each time as such that the mean of Z becomes 1. How to do that? Which random selection method is useful in this case?
With replacement, because I would later also need to know which barrels have appeared the most and which ones are never selected etc.