Answer
$0.233\lt\mu\lt0.401$
Work Step by Step
1. We have $\hat p=\frac{65}{205}=0.317, \hat q=1-\hat p=0.683 , n=205 $
2. At a 99% confidence the critical z-value is $z_{\alpha/2}=2.575$
3. The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=2.575\times\sqrt {\frac{0.317\times0.683}{205}}=0.084$
4. Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.233\lt\mu\lt0.401$
5. The number from the Time magazine, $37\%$, is in the interval.
