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L8_ECE4001_Fall_2008

L8_ECE4001_Fall_2008 - Normal Distribution Probability...

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Slide #1 ECE 4001 L8 © 2008 Lecture 8 Basic Probability Concepts Slide #2 ECE 4001 L8 © 2008 Normal Distribution ( ) 2 2 2 1 P( ) 2 where is the mean value of the variable and is the standard deviation of the variable Probability density function for a normal distribution is give . y n b y y y y y y y e μ σ σ π μ σ - - = P( ) y y y σ - y σ μ Slide #3 ECE 4001 L8 © 2008 Web Based Probability Calculator Slide #4 ECE 4001 L8 © 2008 Transformation From The Normal Distribution To The Standard Normal Distribution Assume we have a of the variable with: mean value of standard de Normal Distribution Standard Normal Distr viation of The is the transformation from to via: ibution Th e y y y y y y y y z y z μ σ μ σ = = - = Standard Normal Distribution has a mean of zero and a standard deviation of 1!
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Slide #5 ECE 4001 L8 © 2008 * * What is the probability , where is some specific value of ? y y y y > * * Pr( ) Pr( ) y y z z > = > Slide #6 ECE 4001 L8 © 2008 Z Table (Posted on WebCT) Slide #7 ECE 4001 L8 © 2008 Z Table Example - z* = 0.75 Slide #8 ECE 4001 L8 © 2008 Some Z Table Values (Table 5.1 of Hyman) 0.0027 0.00135 3.0 0.0124 0.0062 2.5 0.046 0.023 2.0 0.134 0.067 1.5 0.318 0.159 1.0 0.616 0.308 0.5 1.0 0.5 0 Two sided probability One sided probability z* 1 σ 2 σ 3 σ
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Slide #9 ECE 4001 L8 © 2008 USL, LSL, and Tolerance LSL = Lower specification limit, USL = Upper specification limit Standard tolerance values assume: Tolerance 3 or 3 y y y y σ σ = ± Δ = ± Δ = μ LSL -3 σ USL 3 σ Slide #10 ECE 4001 L8 © 2008 Resistor Example ( ) 4 A batch of resistors is specified as 10 Kohm 5% Find the tolerance R, and . R 10 0.05 500 ohms 10 Kohm Assume the tolerance, R, represents 3 , which implies that for a large batch of resistors, al μ σ μ σ ± Δ Δ = = = Δ l but 0.3% will fall between 9.5 Kohm and 10.5 Kohm, and R 500
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