The "3σ" Rule (Empirical Rule) for Normal Distribution
Formula: P(μ - σ < X < μ + σ) ≈ 0.6826 P(μ - 2σ < X < μ + 2σ) ≈ 0.9544 P(μ - 3σ < X < μ + 3σ) ≈ 0.9974 Conditions: Random variable X follows a normal distribut…
Syllabus path: Probability and Statistics › Normal Distribution
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CSCA Mathematics Formula Reference
Formula and explanation
Formula: P(μ - σ < X < μ + σ) ≈ 0.6826 P(μ - 2σ < X < μ + 2σ) ≈ 0.9544 P(μ - 3σ < X < μ + 3σ) ≈ 0.9974 Conditions: Random variable X follows a normal distribution N(μ, σ²). Brief Description: This rule describes the probability of data falling within specific standard deviation ranges around the mean. It is a key property of the normal distribution, used for quick probability estimation and outlier identification.
Related tutorial and examples
Normal Distribution
Normal Distribution 1. Core Concepts and Graph Features The Normal Distribution (or Gaussian Distribution) is the most important continuous distribution. Its probability density curve is Bell - shaped. It is denoted as X ≈ N(μ, σ²). Mean ( μ ): Determines the central location of …
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