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It determines the total area under the curve. The entire area = 1, corresponding to 100%. As the value of σ increases, the normal distribution becomes more spread out.
If the total area under the bell curve adds up to 100%, then 68% of it lies between -1 and +1 standard deviation (SD), 95% between -2 and +2 SD, and 99.7% between -3 and +3 SD.