Answer
$0.1885\lt p\lt0.2865$
The above interval contains $20.4\%$
Work Step by Step
We have $\hat p=0.\frac{95}{400}=0.2375, \hat q=1-\hat p=0.7625 , n=400 $
At a 98% confidence the critical z-value is $z_{\alpha/2}=2.326 $
The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=2.326\times\sqrt {\frac{0.2375\times0.7625}{400}}=0.049$
Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.1885\lt p\lt0.2865$
It can be seen that the above interval contains $20.4\%$
