Answer:
The answer is "16, 43, and 96".
Step-by-step explanation:
Given:
[tex]\sigma = 0.20\\\\c = 95\% = 0.95\\\\\therefore \alpha = 1- c = 1- 0.95 = 0.05\\\\\therefore \frac{\alpha}{2} = 0.025\\\\[/tex]
Using Z table:
[tex]\therefore Z_{\frac{\alpha}{2}} = 1.96\\\\[/tex]
For point a:
[tex]E = 0.10\\\\n=(\frac{Z_{\frac{\alpha}{2} \times \sigma}}{E})^2[/tex]
[tex]= (\frac{(1.96\times 0.20)}{0.10})^2\\\\= 15.3664 \approx 16[/tex]
so, The Sample size (n) = 16
For point b:
[tex]E = 0.06\\\\n=(\frac{Z_{\frac{\alpha}{2} \times \sigma}}{E})^2[/tex]
[tex]= (\frac{(1.96\times 0.20)}{0.06})^2\\\\= 42.6844444444\approx 43[/tex]
For point c:
[tex]E = 0.04\\\\n=(\frac{Z_{\frac{\alpha}{2} \times \sigma}}{E})^2[/tex]
[tex]= (\frac{(1.96\times 0.20)}{0.04})^2\\\\= 96.04\approx 96[/tex]
