Answer
$0.529\lt\mu\lt0.591$
Work Step by Step
1. We have $\hat p=0.56, \hat q=1-\hat p=0.44 , n=982 $
2. At a 95% confidence the critical z-value is $z_{\alpha/2}=1.96 $
3. The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=1.96\times\sqrt {\frac{0.56\times0.44}{982}}=0.031$
4. Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.529\lt\mu\lt0.591$
