NormalApproximationtoBinomial

# NormalApproximationtoBinomial - Normal Approximation to the...

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Normal Approximation to the Binomial Distribution Using the Central Limit Theorem Assume that I select a random sample of size n from a population, where n is “large.” For each member of the sample, I want the answer to a yes-or-no question. For sample member i, let 1 = i X , if the person says, “Yes,” or 0 = i X , if the person says, “No.” Assume that the fraction of members of the population who would give “Yes” answers is p. i) There is a fixed number, n, of trials. ii) The trials are identical to each other, since each one consists of randomly selecting a member of the population and asking the yes-or-no question. iii) The trials are independent of each other, due to random sampling. iv) Each trial has two possible outcomes: Success = {person says, “Yes”} or Failure = {person says, “No”}. v) P(Success) = p for each trial, due to random sampling. Let = = n i i X Y 1 . Then Y ~ Binomial( n, p). The mean of this distribution is np = μ , and the standard deviation is

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## This note was uploaded on 07/28/2011 for the course STA 2014 taught by Professor Staff during the Fall '10 term at University of Florida.

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NormalApproximationtoBinomial - Normal Approximation to the...

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