Last updated: March 2, 2026 by Dr. David Park

The Normal (Gaussian) Distribution

Formula

Z = (X - mu) / sigma.
The Z-score tells how many standard deviations a value is from the mean.

The normal distribution, also known as the Gaussian distribution or bell curve, is the most important probability distribution in statistics. It is defined by two parameters: the mean and the standard deviation.

Approximately 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three, known as the 68-95-99.7 rule.

Common use cases:

  • Standardized test scoring
  • Quality control process limits
  • Financial risk modeling

Frequently Asked Questions

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Dr. David Park

Applied Mathematician, PhD Mathematics

David holds a PhD in Applied Mathematics from MIT. He has published research on numerical methods and computational algorithms used in engineering and scientific calculators.

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