x=500,n=812,95% confidence
p^=xn=500812=0.6158.\hat p=\frac{x}{n}=\frac{500}{812}=0.6158.p^=nx=812500=0.6158.
95%CI=(p^−1.96p^(1−p^)n,p^+1.96p^(1−p^)n)=95\%CI=(\hat p-1.96\sqrt{\frac{\hat p(1-\hat p)}{n}}, \hat p+1.96\sqrt{\frac{\hat p(1-\hat p)}{n}})=95%CI=(p^−1.96np^(1−p^),p^+1.96np^(1−p^))=
=(0.6158−1.960.6158(1−0.6158)812,0.6158+1.960.6158(1−0.6158)812)==(0.6158-1.96\sqrt{\frac{0.6158(1-0.6158)}{812}}, 0.6158+1.96\sqrt{\frac{0.6158(1-0.6158)}{812}})==(0.6158−1.968120.6158(1−0.6158),0.6158+1.968120.6158(1−0.6158))=
=(0.5823,0.6492).=(0.5823,0.6492).=(0.5823,0.6492).
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