Answer
117,102. 102 seems to be better because it uses both methods.
Work Step by Step
$\alpha=1-0.95=0.05.$ Using the table: $z_{\alpha/2}=z_{0.025}=1.96.$
Standard deviation=$\frac{range}{4}=\frac{90-46}{4}=11.$
Hence the sample size this way:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{1.96\cdot11}{2}\right)^2\approx117$.
Using the sample standard deviation:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{1.96\cdot10.3}{2}\right)^2\approx102$. 102 seems to be better because it uses both methods.
