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.

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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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