Elementary Statistics (12th Edition)

a)$\alpha=1-0.98=0.02.$ Then, by using the table, the critical value: $z_{\alpha/2}=z_{0.01}=2.33.$ Hence the minimum sample size: $\frac{z_{\alpha/2}^2\cdot \sigma}{E^2}=\frac{2.33^2\cdot 0.25}{0.05^2}\approx543$. b)$\alpha=1-0.98=0.02.$ Using the table: $z_{\alpha/2}=z_{0.01}=2.33.$ Hence the minimum sample size:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{2.33\cdot 337}{50}\right)^2\approx247$. c) We need to use the maximum out of a) and b), which is 543.