Improvements made to line A had the effect of increasing the proportion $p$ of defect-free components. To estimate this proportion, a random sample of 400 components manufactured by line A is taken. In this sample, the observed frequency of defect-free components is 0.92.

\begin{enumerate}
  \item Determine a confidence interval for the proportion $p$ at the $95\%$ confidence level.
  \item What should be the minimum sample size so that such a confidence interval has a maximum amplitude of 0.02?
\end{enumerate}