For example a resistor of 1kohm with uncertainty of +/- 1%, does this mean in 68% of cases = 1 standard deviation, the resistance will vary by +/- 1%, or does it mean in 95% of cases = 2 standard deviations or is it in 99% of cases = 3 standard deviations the resistance will vary by +/- 1% ?
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It's not an uncertainty; it's a tolerance; a limit. – Andy aka Jan 03 '21 at 18:07
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The tolerance of 1% tells you nothing about the statistics of the actual values. The mean of the actual values might not be the nominal value. The distribution of actual values might not be gaussian and might not be uniform, either.
The tolerance of 1% is telling you that the manufacturer guarantees that all actual values are within 1% of the nominal value, nothing more.
Elliot Alderson
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Parts manufactured that were not within 1% were sold as looser tolerance parts (e.g. 5%), or discarded. – Mattman944 Jan 03 '21 at 18:07
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Or rejects marked with 2% sold as good parts prior to printing after sample tests – Tony Stewart EE75 Jan 03 '21 at 18:10