[tex]\begin{gathered} ME=z\cdot\sqrt[]{\frac{p\cdot q}{n}} \\ 0.05=1.96\cdot\sqrt[]{\frac{0.5\cdot(1-0.5)}{n}} \\ 1.96\sqrt{\frac{0.5\cdot\:0.5}{n}}\cdot\: 100=0.05\cdot\: 100 \\ \\ 196\sqrt{\frac{0.5\cdot\:0.5}{n}}=5 \\ \sqrt{\frac{0.5\cdot\:0.5}{n}}=\frac{5}{196} \\ \frac{0.25}{n}=\frac{25}{38416} \\ n=\frac{9604}{25}=384.16=385 \end{gathered}[/tex]
