17.3 Norm Apprx

17.3 Norm Apprx - Normal Distributions and Approximation to...

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Click to edit Master subtitle style 1/5/10 Normal Distributions and Approximation to Binomial Week of March 16
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1/5/10 Example Suppose X~N(5,16) a) Find k so that P(X < k) = 0.95 Here we are given a probability, and are asked to find an ordinate. Let’s work backwards:
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1/5/10 b) Find k so that P(3 < X < k) = 0.6 0.6 = P(3 < X < k) = P(X < k) - P(X < 3) c) Find k so that P(3 < X < k) = 0.8 Following the same procedure as last time: 0.8 = P(3 < X < k) = P(X < k) - P(X
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1/5/10 Example Suppose X~N(6,9) a) Find k so that P( 6-k < X < 6+k ) = 0.95 Notice that the mean is 6, and we From the tables: P(Z<1.96) = 0.975 thus P(Z < -1.96) = 0.025 P( (X-6)/3 < -1.96) P( X < (3)(- 1.96)+6 ) = 0.025 P( X < 0.12) = 0.025
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1/5/10 The Normal Approximation to We have learned how to find cumulative probabilities of Binomial random variables using the Poisson approximation. Unfortunately, the Poisson approximation does not always hold. In many cases we can use the Normal distribution to approximate the Binomial as well.
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This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.

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17.3 Norm Apprx - Normal Distributions and Approximation to...

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