NormalApproximationtoBinomial

NormalApproximationtoBinomial - Normal Approximation to the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

NormalApproximationtoBinomial - Normal Approximation to the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online