In mathematical notation, these facts can be expressed as follows, where Pr() is the probability function, [1] Χ is an observation from a normally distributed random variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation: The usefulness of this heuristic especially depends on the question under consideration. In the social sciences, a result may be considered ”significant” if its confidence level is of the order of a two-sigma effect (95%), while in particle physics, there is a convention of a five-sigma effect (99.99994% confidence) being required to qualify as a discovery. Contents. Proof Edit. 1 2 π ∫ − n n e − u 2 2 d u , >>\int _^e^>>>du\end>,> Pr ( μ − 1 σ ≤ X ≤ μ + 1 σ ) = 1 2 π ∫ − 1 1 e − u 2 2 d u ≈ 0.6827 Pr ( μ − 2 σ ≤ X ≤ μ + 2 σ ) = 1 2 π ∫ − 2 2 e − u 2 2 d u ≈ 0.9545 Pr ( μ − 3 σ ≤ X ≤ μ + 3 σ ) = 1 2 π ∫ − 3 3 e − u 2 2 d u ≈ 0.9973. Joined ação de regresso taxa condominial apos o registro no cartorio Aug 21, 2022 Messages 628. For example, Φ (2) ≈ 0.9772 , or Pr( X ≤ μ + 2 σ ) ≈ 0.9772 , corresponding to a prediction interval of (1 − (1 − 0.97725)·2) = 0.9545 = 95.45% .
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