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

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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....

What is Standard Normal Distribution?

Standard Normal Distribution, often referred to as the Z-Distribution, is a specific type of normal distribution that has a mean (μ) of 0 and a standard deviation (σ) of 1....

Standard Normal Distribution Table

Standard Normal Distribution Table which is also called, Standard Normal Distribution Z Table is the table of z-value for standard normal distribution where Z = [(x-μ)/σ]. The Standard Normal Distribution Z Table is given as follows:...

Area of Standard Normal Distribution

The table given above is used to calculate the “Area of Standard Normal Distribution” curve. It is basically used to find the area from –∞ to Z. So we can say...

Standard Normal Distribution Function

Standard Normal Distribution Function is added below:...

Application of Standard Normal Distribution

Standard Normal Distribution has a wide range of applications and usage in several fields. Here are some important applications:...

Characteristics of Standard Normal Distribution

Standard normal distribution is defined by the following characteristics:...

Standard Normal Distribution Examples

Let’s solve some problems on Standard Normal Distribution...

FAQs on Standard Normal Distribution

What is Standard Normal Distribution?...