The margin of error is given by the formula
[tex] ME=z_{\alpha /2}\frac{\sigma}{\sqrt{n}} [/tex]
Solving for n,
[tex] n=z^2_{\alpha /2}\frac{\sigma^2}{ME^2} [/tex]
Here [tex] 1-\alpha =0.6826\\
\alpha =0.3174 [/tex]
Using standard normal table [tex] z_{\alpha /2}=-1 [/tex]
[tex] \sigma^2=13,ME=2 [/tex]
Substituting numerical values,
[tex] n=(-1)^2\frac{13}{2^2} \approx 4 [/tex]
