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Random fluctuations result in a distribution of results when making repetitive measurements. The distribution that results due to truely random events is called a "normal error" or Gaussian curve. It is also sometimes called a "bell-shaped curve". The mathematical expression for this random distribution is:
Where is the population standard deviation:
and with µ being the population mean.
This equation is plotted below. The dark vertical lines indicate the area under the curve from -1 to +1, and the lighter lines indicate the area under the curve for ±2.
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