Answer
154
Work Step by Step
Given $E=0.25,\sigma=1.2$, at the 99% confidence, the critical z-value is $z_{\alpha/2}=2.58$
and we have the equation for the margin of error $E=2.58\times\frac{1.2}{\sqrt {n}}=0.25$ which gives
$n=(\frac{2.58\times1.2}{0.25})^2=153.4\approx154$ (round up to the next integer here)