Answer:
We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%
Explanation:
-From the given information,
.
-We calculate the confidence interval using this value at 95% confidence level:
![CI=\hat p\pm z \sqrt{(\hat p(1-\hat p))/(n)}\\\\\\=0.65\pm 1.96* \sqrt{(0.65* 0.35)/(12000)}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585]](https://img.qammunity.org/2021/formulas/mathematics/college/f9zusudaim1d4o4uq0ub0jpd14mffdyfv9.png)
So, the 95% confidence interval is (0.6515,0.6585).
Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.