- #1
matt grime said:To view the question slightly differently, have you plotted histograms of binomial distributions for a large number of trials? It approximates the normal distribution, ie the graphs agree, and it can be shown that as n goes to infinity that the exponential formula is "correct" (ie the error in using it goes to zero.
A normal distribution derivation is a mathematical process used to derive the formula for the probability density function of a normal distribution. It involves using calculus and statistical concepts to determine the shape and characteristics of a normal distribution.
The assumptions made in a normal distribution derivation include:
A normal distribution is derived by using the properties of a Gaussian curve, such as its symmetry and the area under the curve being equal to 1. The derivation involves manipulating the formula for a Gaussian curve, using calculus to find the maximum point of the curve, and then using the mean and standard deviation to shift and scale the curve to fit the data.
The normal distribution is important in statistics because it is a commonly occurring distribution in nature and is often used to model real-world phenomena. Many statistical tests and methods rely on the assumption of normality, and the ability to use the normal distribution allows for simpler and more accurate analyses.
Some real-world applications of normal distribution derivation include: