Mathematical Analysis of the Normal Distribution Curve

Mathematical analysis of the normal distribution curve has produced data tables which provide population statistics in relation to multiples of the standard deviation. For example, 68.3 per cent of the population lies within ±1 standard deviation of the mean; 95.4 per cent lies within ±2 standard deviations, and 99.7 per cent lies within ±3 standard deviations (as shown in this figure). As will be seen later, SPC charts use multiples of ±1.96σ and ±3.09σ to set the control chart limits.

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