1. Find the sample proportion:
[tex]\frac{212}{400}=0.53[/tex]2. Find the z-critical value for 95% confidence:
For 95% confidence interval the z-critical value is 1.96
3. Use the next formula to find the Confidence interval (CI):
[tex]CI=Sample\text{ }proportion\pm z-critical*\sqrt{\frac{sample\text{ }proportion*(1-sample\text{ }proportion)}{sample\text{ }size}}[/tex][tex]\begin{gathered} CI=0.53\pm1.96*\sqrt{\frac{0.53(1-0.53)}{400}} \\ \\ CI=0.53\pm1.96*\sqrt{\frac{0.53*0.47}{400}} \\ \\ CI=0.53\pm0.049 \\ \\ CI=(0.481,0.579) \end{gathered}[/tex]