The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, which is symmetric around the mean.
It describes how the values of a variable are distributed and is widely used in statistics and natural and social sciences.
Formula
Application
The normal distribution is used in various fields to model real-valued random variables whose distributions are not known.
Applications include:
Heights and weights of individuals
Blood pressure readings
Test scores
Measurement errors
Properties
Symmetry: The distribution is symmetric about the mean.
Mean, Median, Mode: All are equal and located at the center of the distribution.
Empirical Rule: Approximately 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.
Normal Curve
The normal curve is a graphical representation of the normal distribution. It is bell-shaped and centered at the mean (μ), with the spread determined by the standard deviation (σ).
