Answer
a) 271
b)139
c)No.
Work Step by Step
If $\hat{p}$ is known:$n=\frac{z^2_{\frac{\alpha}{2}}\cdot \hat{p}\cdot (1-\hat{p})}{E^2}.$
If $\hat{p}$ is unknown:$n=\frac{z^2_{\frac{\alpha}{2}}\cdot0.25}{E^2}.$
a) Here, $\hat{p}$ is unknown, hence $n=\frac{1.645^2\cdot0.25}{0.05^2}=271.$
b)Here, $\hat{p}$ is known, it is 85%=0.85, hence $n=\frac{1.645^2\cdot(0.85)\cdot(1-0.85)}{0.05^2}=139.$
c)This survey uses a convenience sample, whoch doesn't represent the entire population correctly.
