Suppose we have normal distribution of measured data. We know what the standard deviation is for the whole distribution precisely from an infinitely largye number of measurement.
We carry out one measurement. The result is x1.
The expected value (the precise mean from a large number of measurements) will be in the range of x1±2SD at a probability of approximately 95.449 %.
The next measurement result x2 will fall in a range around x1 at a probability of 95.449 %. This range is x1±4SD.
Am I right?
In other words, if I know the SD of the distribution and I have one data x1 what can I expect for my next data x2? How far this x2 could be from my one and only result.
Thank you very much for your professional consideration.
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