Characteristics of Standard Normal Distribution
Standard normal distribution is defined by the following characteristics:
- Mean: The mean (average) is 0 that is symbolically represented as μ = 0.
- Standard Deviation: The standard deviation is 1 that is symbolically represented as σ = 1.
- Symmetry: It is symmetric around the mean (μ = 0).
- Bell-Shaped Curve: The graph is bell-shaped, that means most values cluster around the mean (μ = 0).
- Total Area Under Curve: The total area under the curve is 1, representing the total probability.
- 68-95-99.7 Rule: Approximately 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
- Asymptotic: The tails of the distribution approach, but never touch, the horizontal axis.
- Unimodal: It has a single peak at the mean (μ = 0).
- Standard Scores (Z-Scores): Any normal distribution can be transformed into the standard normal distribution using z-scores where z = (x – μ)/σ.
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