A normal distribution is a continuous probability distribution characterized by its symmetric bell shape and defined by its mean and standard deviation.
The normal distribution is a continuous probability distribution that is symmetric around its mean, often visualized as the classic bell curve.
Its defining feature is that it is fully described by two parameters: the mean (μ) and the standard deviation (σ).
These parameters determine the center and spread of the distribution, respectively.
What makes the normal distribution special is the empirical rule: approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.
This property allows you to make predictions about data behavior.
The challenge is recognizing when a dataset is approximately normal and when it isn't.
Real-world data rarely fits perfectly, so you need to assess normality using histograms, normal probability plots, or calculating skewness and kurtosis.
Misjudging normality leads to incorrect conclusions about variability and probability, especially when computing z-scores or using the distribution to estimate population parameters.