Answer: 385
Step-by-step explanation:
If the prior estimate of population proportion is unknown , then the formula to find the minimum sample size is given by :-
[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2[/tex]
where, [tex]z_{\alpha/2}[/tex] is the z-value for significance level([tex]\alpha[/tex]) and E = the margin of error .
Given : Confidence level = 0.95
significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical z-value for 95% confidence level : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]
Margin of error : E= 0.05
Also, prior population proportion is unknown.
Required sample size : [tex]n=0.25(\dfrac{1.96}{0.05})^2[/tex]
Simplify ,
[tex]n=384.16\approx385[/tex]
Hence,You would survey 385 drivers.
