Answer
84245. This sample is huge and hence not too practical.
Work Step by Step
$\alpha=1-0.99=0.01.$ Using the table: $z_{\alpha/2}=z_{0.005}=2.58.$
Standard deviation=$\frac{range}{4}=\frac{45000-0}{4}=11250.$
Hence the sample size:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{2.58\cdot11250}{100}\right)^2\approx84245$. This sample is huge and hence not too practical.
