Part of the city's DVD stock consists of animated films intended for young audiences. An animated film is chosen at random and we denote by $X$ the random variable that gives the duration, in minutes, of this film. $X$ follows a normal distribution with mean $\mu = 80$ min and standard deviation $\sigma$. Furthermore, it is estimated that $P(X \geqslant 92) = 0{,}10$.

\begin{enumerate}
  \item Determine the real number $\sigma$ and give an approximate value to 0.01.
  \item A child watches an animated film whose duration he does not know. Knowing that he has already watched one hour and thirty minutes, what is the probability that the film ends within the next five minutes?
\end{enumerate}