Analytical Chemistry

A Little Math

What is the area under the curve for a normalized Gaussian distribution?

As should be the case for any normalized probability distribution, the area under the curve of a Gaussian distribution totals to 1. This is necessary for the probability of a set of events to have a physically meaningful value since the sum of the probabilities of all possible outcomes must total to 1 (or 100%). Probability distributions that satisfy this property are said to be normalized, and the Gaussian distribution is actually also commonly referred to as the normal distribution. With any Gaussian distribution, 68% of the possible outcomes will lie within 1 standard deviation of the mean value, 95% within two standard deviations, and 99.7% within three standard deviations.


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