The confidence interval for a population proportion is given as:
[tex]p=p^{\prime}\pm\mleft[Z_{(\frac{a}{2})}\frac{\mleft(\mright?_{}p^{\prime}\mleft(1-p^{\prime}\mright)}{n}\mright][/tex]where:
p' = sample proportions = 0.5
n = sample size = 510
z = z score = 2.576
Hence, we have:
[tex]\begin{gathered} p=0.5\pm\lbrack2.576\times\frac{0.5\times0.5}{510}\rbrack \\ p=0.50126\text{ or 0.49}874 \\ p=50.126\text{ \% or 49.874\%} \end{gathered}[/tex]