Lecture26[1]

# Lecture26[1] - Lecture 26 Normal Approximations Section 6.3...

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Normal Approximations Lecture 26 Section 6.3

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Normal Approx. to the Binomial For a random variable as the PMF of the Binomial becomes very similar in shape to the Normal PDF. Due to this similarity, we can use a Normal random variable to approximate a Binomial random variable if n is large and p is reasonable close to 0.5 (not close to 0 or 1). ~ ( , ) X Bin n p n 
Normal Approx. to the Binomial General conservative guidelines for use: np > 5 n (1- p ) > 5 The larger n is, the more precise the approximation will be. Here is an applet to show examples. http://www.stat.wvu.edu/SRS/Modules/NormalAp prox/normalapprox.html

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Normal Approx. to the Binomial ~ ( , ) X Bin n p ( , (1 )) X N np np p  If Then Mean of a binomial Variance of a binomial
Continuity Correction There is one more important detail that we have to take care of when computing Normal approximations of Binomial RV’s When X is Binomial, it is a discrete random variable where as a Normal distribution is a continuous random variable.

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Continuity Correction
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## This note was uploaded on 05/19/2011 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University-West Lafayette.

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Lecture26[1] - Lecture 26 Normal Approximations Section 6.3...

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