LEC16 Normal Dist

LEC16 Normal Dist - The Normal Distribution A continuous...

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Unformatted text preview: The Normal Distribution A continuous normal r.v. X has probability density function ( 29 f x e x x ( ) =- < < -- 1 2 2 2 2 parameters: - < < and >0. E(X)= and V(X)= 2 Normal Distribution f(x) x When Does the Normal Distribution Arise Measurement is subject to sources of error that are many sources of variation independent sources each source contributes a small variation Example: dimension of a machined part is subject to variations in temperature humidity vibrations cutting angle cutting tool wear bearing wear rotational speed mounting and fixturing raw materials 2 Learn the Probabilities of the Normal Distribution TRUE FOR ANY AND 6 8 % - + P X ( ) . - < < + = 6827 +2 -2 9 5 % P X ( ) . - < < + = 2 2 9545 -3 9 9 % +3 P X ( ) . - < < + = 3 3 9973 3 The Normal Distribution is Symmetrical Find the probability X is greater than +2 . +2 -2 .0 2 5 .9 5 .0 2 5 P(X> +2 ) = .025 Find the probability X is less than +2 . +2 -2 .0 2 5 .9 5 .0 2 5 P(X< +2 ) = .025+.95 = .975 4 The Standard Normal The standard normal distribution has =0 and =1....
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LEC16 Normal Dist - The Normal Distribution A continuous...

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