For your exercise, we have:
E=10
[tex]\sigma=63.4[/tex]n=?
E= margin of error
[tex]E=z.\frac{\sigma}{\sqrt[]{n}}[/tex]For 95% confidence, we have z=1.96 .
Now, let's replace the known data.
[tex]\begin{gathered} 10=1.96.\frac{63.4}{\sqrt[]{n}} \\ 10.\sqrt[]{n}=1.96\cdot63.4 \\ \sqrt[]{n}=\frac{124.264}{10} \\ \sqrt[]{n}=12.4264 \\ (\sqrt[]{n})^2=(12.4264)^2 \\ n=154.4154 \\ n=155 \end{gathered}[/tex]