PPT3 Normal Distribution

PPT3 Normal Distribution - McGill University Advanced...

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McGill University Advanced Business Statistics MGSC-272
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Fall’09 Normal Distribution
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The Normal Distribution aka The Gaussian Distribution
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The Normal Distribution 2 1 2 1 ( ) 2 x f x e μ σ πσ - - ÷ = x y
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Areas under the Normal Distribution curve + +2 +3 - - 2 -3 68% 95% 99.7% X = N( , 2 )
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Determining Normal Probabilities Since each pair of values for μ and σ represents a different distribution, there are an infinite number of possible normal distributions. The number of statistical tables would be limitless if we wished to determine probabilities for all of them. The standard normal distribution z has a mean of 0 and a standard deviation of 1, i.e. z = N(0,1), and provides a basis for computing probabilities for all normal distributions. We must therefore convert each normal random variable X into the standard normal random variable z using the standardization formula: x z μ σ - =
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Standardization Formula x z μ σ - = The standardization formula converts a normal distribution x = N( , 2 ) into the standard normal distribution z = N(0,1) 2 1 2 1 2 z z e π - =
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Standard Normal Distribution Areas 0 1 2 3 -1 -2 -3 68% 95% 99.7% z = N(0,1)
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PPT3 Normal Distribution - McGill University Advanced...

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