Answer
$(0.7319,0.7881)$
Work Step by Step
$\hat{p}=\frac{x}{n}=\frac{475}{625}=0.76$
The z-value belonging to the $90\%$ confidence interval according to the table is $z=1.645$, thus the confidence interval is: $\hat{p}\pm z\sqrt{\frac{p(1-p)}{n}}$, which here is: $0.76\pm 1.645\sqrt{\frac{0.76\cdot(1-0.76)}{625}}$, thus the confidence interval is $(0.7319,0.7881)$
