Answer:
The correct answer to the following question will be "384".
Step-by-step explanation:
We are having,
[tex]P(-0.05<p-p<0.05)=0.95[/tex]
On solving, we get
⇒ [tex]P(\frac{-0.05}{\sqrt{\frac{pq}{n}}}<Z<\frac{-0.05}{\sqrt{\frac{pq}{n}}}=0.95)[/tex]
⇒ [tex]\frac{0.05}{\sqrt{\frac{p(1-p)}{n}}} =1.96[/tex]
On applying cross-multiplication, we get
⇒ [tex]0.05^2=1.96^2\times \frac{P(1-p)}{n}[/tex]
⇒ [tex]0.05^2n=1.96^2-1.96^2p^2[/tex]
⇒ [tex]1.96^2p^2-1.96^2p+0.05^2n=0[/tex]...(equation 1)
When "p" seems to be the population proportion, (equation 1) approach, which is special
∴ [tex]b^2-4ac=0[/tex]
On putting the values in the above expression, we get
⇒ [tex](1.96)^4-4\times 0.05^2\times 1.96^2n=0[/tex]
⇒ [tex]1.98^2-4\times 0.05^2n=0[/tex]
⇒ [tex]n=\frac{1.96^2}{4\times 0.05^2}[/tex]
⇒ [tex]n=384.16=384[/tex]
