Probability - Normal approx. to the Binomial

1

• Probability - Normal approx. to the Binomial
• Recall that if Y is B(n,pi), then
  P(Yy)dbinom(y,n,pi). So plot a few of these
  distributions for n20 and pi.1,.25,.5,.8 e.g.,
  
• plot(020,dbinom(020,20,.1),typel)
• from this you can see the approx. normality.
• so what is the mean and s.d. of the approximating
  normal?? use the mean and s.d. of the Binomial
  meann(pi) sdsqrt(n(pi)(1-pi)). For the above
  example, mean2, s.d.1.341641
• most rules of thumb would say use this
  approximation only when npigt5 and n(1-pi)gt5
• but in an R world where we can compute exact
  values of all binomial distributions, the use of
  the normal approximation is of theoretical
  interest only in the context of inference