Normal Distribution and CHEBYSHEV’S Inequality
Normal Distribution : The Normal distribution also called Gaussian distribution was named after Johann Carl Friedrich Gauss, a German mathematician.
The Gaussian distribution, also known as the normal distribution, is the most important of all probability distributions, as it can be used to describe a very large variety of random phenomena in areas of science, engineering, social sciences, business, and medicine.
In a normal distribution
1)About 68% of the data lies within one standard deviation of the mean
2) About 95% lies within two standard deviations
3) About 99.7% of the data with in three standard deviations
Just knowing the number of standard deviations from the mean can give you a rough idea about the probability.
CHEBUSHEV’S Inequality : This rule can be applied to any distribution . It states that for any distribution
1)At least 75% of your values lie within 2 standard deviations of the mean
2) At least 89% of your values lie within 3 standard deviations of the mean
3) At least 94% of your values lie within 4 standard deviations of the mean
This rule is not precise as Normal distribution as it only gives you minimum percentages but gives rough idea of where values fall in probability distribution
