@edgarthendoschool,
You don't have an infinite number of bags. If you did, your +/- three sigma argument would be reasonable. Since you have a finite set of bags, it could be that they all fit inside 2.5 sigma on either side which would be 40, not 48. That is the thing with statistics, it describes what is likely to be, not what is. The chance of getting a value outside of 2.6 sigma is one percent. If you take a hundred samples, you would expect one of them to be outside 2.6 sigma, but if you calculate the stats, there is over a 30% chance that none of them will be. If you take 200 samples there is still a ten percent chance that you will not have any outside of 2.6 sigma. If you really want to prove this to yourself, it would be easy to make a hundred random weights in Excel and see how many times it falls outside the range.
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