Refer to Exercise 7.70.a For what values of n will the

Chapter 7, Problem 71E

(choose chapter or problem)

 

In this section, we provided the rule of thumb that the normal approximation to the binomial distribution is adequate if \(p \pm 3 \sqrt{p q / n}\) lies in the interval (0, 1) — that is, if

\(0<p-3 \sqrt{p q / n} \text { and } p+3 \sqrt{p q / n}<1\)

Show that

\(p+3 \sqrt{p q / n}<1\)  if and only if \(n>9(p / q)\)

Show that

\(0<p-3 \sqrt{p q / n}\) if and only if \(n>9(p / q)\)

      (c) Combine the results from parts (a) and (b) to obtain that the normal approximation to  

           the binomial is adequate if

\(n>9\left(\frac{p}{q}\right) \text { and } n>9\left(\frac{q}{p}\right)\),

        oe , equivalently,

\(n>9\left(\frac{\text { larger of pand } q}{\text { smaller of p and } q}\right)\)

Equation Transcription:

     

     

         

Text Transcription:

p \pm 3 \sqrt p q / n

\(0<p-3 \sqrt p q / n and p+3 \sqrt p q / n<1\)

p+3 \sqrt p q / n<1

n>9(p / q)

0<p-3 \sqrt p q / n

n>9(p / q)

n>9\(\p q) and n>9(q p\right)

n>9\(\larger of p and  q \ smaller of p and  q\right