Applications of the Normal Distribution in Chemistry and Physics

The most important results of the last section can be summarized as follows  

The likely fluctuation from the most probable result is proportional to the square root of the number of random events (VW). 

The probability of observing a fluctuation which is much larger than the standard deviation a is extremely small. 

These results turn out to be applicable to much more than just coin toss problems. A few examples are given below. 

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Section 4.3 Applications of the Normal Distribution in Chemistry and Physics... 

Just as logarithms and exponentials are inverse operations, integration is the inverse of differentiation. The integral can be shown to be the area under the curve in the same sense that the derivative is the slope of the tangent to the curve. The most common applications of integrals in chemistry and physics are normalization (for example, adjusting a probability distribution so that the sum of all the probabilities is 1) and calculation of the expectation values of observable quantities. 

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