What Normal Distribution Meaning, Applications & Example
A bell-shaped probability distribution used in statistics.
What is Normal Distribution?
Normal Distribution, also known as Gaussian distribution, is a continuous probability distribution that is symmetric about the mean. It is one of the most important and widely used distributions in statistics, especially in hypothesis testing and statistical modeling. The shape of the normal distribution curve is bell-shaped, with most of the data points clustering around the mean and fewer points found as you move away from the mean in either direction.
Key Properties of Normal Distribution
- Mean, Median, and Mode: In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.
- Symmetry: The curve is symmetric around the mean, meaning the left and right halves are mirror images.
- 68-95-99.7 Rule: About 68% of the data falls within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
- Bell-shaped Curve: The curve of the normal distribution is smooth and bell-shaped, with tails extending infinitely in both directions.
Applications of Normal Distribution
- Statistical Inference: Many statistical tests, such as t-tests and ANOVA, assume the data follows a normal distribution.
- Quality Control: Normal distribution is used in manufacturing to model and control product quality, ensuring most products meet specifications.
- Finance: In finance, the normal distribution is used to model the returns of assets and to assess the risk and volatility of investments.
- Psychometrics: Standardized tests, such as IQ tests, are designed based on the assumption that scores follow a normal distribution.
Example of Normal Distribution
In height measurement of adult women in a population, if the heights are normally distributed with a mean of 160 cm and a standard deviation of 5 cm, approximately 68% of women will have heights between 155 cm and 165 cm. The further you go from the mean, the fewer people will fall into those height ranges, as the distribution tails off.