Step 1

Here we need to express the given confidence interval in \(\displaystyle{p}\frac{+}{{-{{E}}}}\) form.

Step 2

a) Here the given \(\displaystyle{C}{I}={\left({0.501},{0.609}\right)}\)

From the given confidence interval.

Point estimate \(\displaystyle{p}={\frac{{{U}+{L}}}{{{2}}}}={\frac{{{0.501}+{0.609}}}{{{2}}}}\)

\(\displaystyle={0.555}\)

\(\displaystyle\therefore{p}={0.555}\)

Now \(\displaystyle{E}={\frac{{{U}+{L}}}{{{2}}}}={\frac{{{0.609}-{0.501}}}{{{2}}}}={0.054}\)

\(\displaystyle\therefore{E}={0.054}\)

\(\displaystyle\therefore{C}{I}={0.555}\pm{0.054}\)

\(\displaystyle={0.501}{<}{p}{<}{0.609}\)

\(\displaystyle{P}\pm{E}={0.555}\pm{0.054}\)