Normal Distribution Definition
Normal Distribution ( or normal random variable) is the most significant continuous probability distribution in the field of statistics. It can also be said as the parent topic to study Standard Normal Distribution. It has a bell-shaped curved graph that roughly characterizes a variety of events seen in science, business, and the natural world.
Now there comes another term which is normal random variable, which is a continuous random variable X with a bell-shaped distribution. The two parameters μ ( symbol for mean for population ) and σ ( symbol for standard deviation for population ) respectively, determine the mathematical formula for the probability distribution of that variable. Therefore, we represent the density values of X by n(x; μ, σ).
Density of normal random variable X, with mean (μ) and variance (σ2), is
n(x; μ, σ) = /√(2πσ), -∞ < x < ∞,
where,
- π = 3.14159…
- e = 2.71828…
Once σ and μ are given, the normal distribution curve can be easily interpreted.
Standard Normal Distribution
Standard normal distribution, also known as the z-distribution, is a special type of normal distribution. In this distribution, the mean (average) is 0 and the standard deviation (a measure of spread) is 1. This creates a bell-shaped curve that is symmetrical around the mean.
In this article we have covered, Standard Normal Distribution definitions, examples, and others in detail
Before starting with Standard Normal Distribution let’s first learn what is meant by Normal Distribution.
Table of Content
- Normal Distribution Definition
- What is Standard Normal Distribution?
- Standard Normal Distribution Table
- Area of Standard Normal Distribution
- Standard Normal Distribution Function
- Application of Standard Normal Distribution
- Characteristics of Standard Normal Distribution
- Standard Normal Distribution Examples
- FAQs on Standard Normal Distribution