TeX source:

\begin{aligned} &{\left[\hat{p}-3 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+3 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right]} \\ &=[0.5255-0.03,0.5255+0.03] \\ &=[0.4955,0.5555] \subset[0,1] \end{aligned}