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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:
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) = P(X < k) - 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 < 3)

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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
1/5/10 The Normal Approximation to the Binomial Distribution 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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1/5/10 Let Y be a Binomial random variable.
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17.3 Norm Apprx - Normal Distributions and Approximation to...

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