Estudou Business and Process Management pela University of Arkansas - EUA, direcionando sua especialização em Lean Seis Sigma. Professor de empresas como BRF, Plasútil, Usiminas, Petrocoque, Avon, Mondelli, UNESP, JohnDeere e de mais de 35.000 alunos na comunidade online. Com mais de 26 mil certificados emitidos, é CEO da CAE Treinamentos, uma plataforma focada em melhoria contínua e gestão de processos. 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: 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. Proof Edit. 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. &\Pr(\mu -1\sigma \leq X\leq \mu +1\sigma )=>>\int _^e^>>>du\approx 0.6827\\&\Pr(\mu -2\sigma \leq X\leq \mu +2\sigma )=>>\int _^e^>>>du\approx 0.9545\\&\Pr(\mu -3\sigma \leq X\leq \mu +3\sigma )=>>\int _^e^>>>du\approx 0.9973.\end>> 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% . This is not a symmetrical interval – this is merely the probability that an observation is less than μ + 2 σ .
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p. 23 – 25. 622 páginas ↑ Saporta, Gilbert (2006). Probabilités – Analyse des Données et Statistiques . Paris: Éditions Technip. p. 26. Fan tan betano.
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