Answer:
[0.4979, 0.5479]
Explanation:
-We first determine the sample proportion:

-The confidence intervals of a sample proportion is calculated using the formula:

#We substitute for the sample proportion and z value to get the Confidence interval:
![CI=\hat p\pm z\sqrt{(\hat p(1-\hat p)/(n)}\\\\=0.5238\pm 1.645* \sqrt{(0.5238*0.4762)/(1008)}\\\\=0.5238\pm0.0259\\\\=[0.4979,0.5497]](https://img.qammunity.org/2021/formulas/mathematics/high-school/lgvpnmjgq3qw6pwyd63qqjvu1p369mi1sl.png)
Hence, the 90% confidence intervals is [0.4979,0.5479]