Answer: 126
Step-by-step explanation:
As per given , we have
Prior Population proportion : [tex]p=\dfrac{1}{5}=0.2[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value for 95% confidence interval (using the z-value table) = [tex]z_{\alpha/2}=1.96[/tex]
Margin of error (maximum error): [tex]E=7\%=0.07[/tex]
Formula to find the sample size :
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\ n=0.20(1-0.20)(\dfrac{1.96}{0.07})^2\\\\ n=125.44\approx126[/tex]
Therefore , the required minimum sample size = 126
