Derivation of Probability pxu

Source: http://mathworld.wolfram.com/ConfidenceInterval.html, reference AB30

Assuming Normal Distribution of results:

Pxu = ERF(n/SQRT(2))

where

• Pxu = probability result x lies within ± n SD of mean u in figure A
• ERF = error function
• n = specified number of Standard Deviations
• SD = Standard Deviation

Substituting #SD for n and taking absolute value of # SD:

Pxu = ERFC(ABS(#SD)/(SQRT(2)))

where

• Pxu = probability each independent result lies within # SD of either side of mean = either half of area under curve in figure B
• # SD = measured difference between any result and the mean

Taking complement of error function to select area outside of confidence interval:

pxu = ERFC(ABS(#SD)/(SQRT(2)))

where

• pxu = probability any result lies outside # SD of either side of mean = either half of area under curve in figure C
• ERFC = complimentary error function = 1 - ERF

pxu = ERFC(ABS(#SD)/(SQRT(2)))

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