The Normal Distribution

In many natural processes, random variation conforms to a particular probability distribution known as the normal (Gaussian) distribution or bell curve. Some of these natural processes are height, weight, test scores, light bulb lifetime and the performance of a diversified investment portfolio. Below is a normal probability distribution for the height of men in the United States. The mean or average height for men is 69.3 inches and the standard deviation is 2.8 inches(1). The standard deviation a measure of the volatility or dispersion of the data. A low standard deviation means the data is close to the average while a high standard deviation means the data is spread across a wide range of values.

Here are some characteristics of the normal distribution

1) It is symmetrical about the mean. The probability of being above the mean is the same as the probability of being below the mean.

2) The curve is completely described by its mean and its standard deviation. Any normal distribution differs from any other normal distribution only by its mean and/or standard deviation.

3) The probability any data is within +/- 1 standard deviation of the mean is 68.27%. For the plot above this would be the probability the height is between 66.5 inches and 72.1 inches.

4) The probability any data is within +/- 2 standard deviations of the mean is 95.45%.For the plot above this would be the probability the height is between 63.7 inches and 74.9 inches.

5) The probability any data is within +/- 3 standard deviations of the mean is 99.73%. For the plot above this would be the probability the height is between 60.9 inches and 77.7 inches.

6) The total area under the curve is equal to the total probability and is therefore equal to one or 100%. The area under any portion of the curve is equal to the probability the data lies within that range. For the plot above, this implies that 100% of the males measured fits in the measured range and that the probability of a male measuring between say 72.1 inches and 74.9 inches is equal to the probability the height is above 72.1 inches (15.87%) minus the probability the height is above 74.9 inches (2.28%) or 13.6%.

(1) https://www.cdc.gov/nchs/fastats/body-measurements.htm

(2) http://www.intmath.com/counting-probability/14-normal-probability-distribution.php

 

Disclosure:

The information presented here is the opinion of the author and may quickly become outdated and is subject to change without notice. All material presented in this article are compiled from sources believed to be reliable, however accuracy cannot be guaranteed. No person should make an investment decision in reliance on the information presented here.

The information presented here is distributed for education purposes only and is not an offer to buy or sell or a solicitation of an offer to buy or sell any security or participate in any particular trading strategy.

Performance data showing past performance results is no guarantee of future returns.

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