Answer
$(153.859,160.141)$
Work Step by Step
$1-\alpha=0.95$, thus according to the table, $z_{\alpha/2}=z_{0.025}=1.96$.
Thus the confidence interval is: $\overline{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt n}$, which here is: $157\pm 1.96\frac{35}{\sqrt{477}}$, thus the interval is: $(153.859,160.141)$