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Normal Distribution (3-Sigma Rule)

正态分布(3σ原则 / 68-95-99.7准则)

P(μ−σ≤X≤μ+σ)≈0.6826andP(μ−2σ≤X≤μ+2σ)≈0.9544

Theoretical Identity Description:

The 3-Sigma (68-95-99.7) rule for a normal distribution with mean 'μ' and standard deviation 'σ'. It describes the percentage of data falling within one, two, and three standard deviations from the mean.

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
P(μ−σ≤X≤μ+σ)≈0.6826andP(μ−2σ≤X≤μ+2σ)≈0.9544

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
P(μ−σ≤X≤μ+σ)≈0.6826

Targeted algebraic evaluation and parameter substitution.

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Normal Distribution (3-Sigma Rule)
正态分布(3σ原则 / 68-95-99.7准则)

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