Answer
$\hat{p} = 0.4855$, E = 0.0235, $x = 816$
Work Step by Step
Lower Bound: 0.462, Upper Bound: 0.509, n =1680
i) Find Error
Width of Interval = Upper Bound - Lower Bound
(0.509 - 0.462) = $\hat{p} + E - (\hat{p} - E)$
0.047 = 2E
E = 0.0235
ii) Find $\hat{p}$
$\hat{p} - E = Lower Bound$
$\hat{p} = Lower Bound + E$
$\hat{p} = 0.462 + 0.0235$
$\hat{p} = 0.4855$
iii) Find $x$
$\hat{p} = \frac{x}{n}$
$x = n\hat{p}$
$x = 1680 \times 0.4855$
$x = 816$
