Answer
E = 0.042
$\hat{p} = 0.554$
Work Step by Step
Lower Bound: 0.596, Upper Bound: 0.512,
i) Find Error
Width of Interval = Upper Bound - Lower Bound
(0.596 - 0.512) = $\hat{p} + E - (\hat{p} - E)$
0.084 = 2E
E = 0.042
ii) Find $\hat{p}$
$\hat{p} - E = Lower Bound$
$\hat{p} = Lower Bound + E$
$\hat{p} = 0.512 + 0.042$
$\hat{p} = 0.554$