Answer
545
Work Step by Step
Given $E=0.03, \hat p=0.15, \hat q=1-\hat p=0.85 $
At a 95% confidence the critical z-value is $z_{\alpha/2}=1.96 $
With $E=0.03,$ the equation $E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}$
becomes $1.96\times\sqrt {\frac{0.15\times0.85}{n}}=0.03$
Thus $n=(\frac{1.96}{0.03})^2\times0.15\times0.85=544.2\approx545$ (round up to the next integer here)