The industrialist claims that only $2\%$ of the valves he manufactures are defective. We assume this claim is true, and we denote $F$ the random variable equal to the frequency of defective valves in a random sample of 400 valves taken from total production.

\begin{enumerate}
  \item Determine the interval $I$ of asymptotic fluctuation at the $95\%$ threshold of the variable $F$.
  \item We choose 400 valves at random from production. We treat this choice as a random draw of 400 valves, with replacement, from production. Among these 400 valves, 10 are defective. In light of this result, can we question, at the $95\%$ threshold, the industrialist's claim?
\end{enumerate}