A factory produces mineral water in bottles. When the calcium level in a bottle is less than $6.5 \mathrm { mg }$ per litre, the water in that bottle is said to be very low in calcium.

Let $X$ be the random variable that, for each bottle randomly selected from the daily production of source A, associates the calcium level of the water it contains. We assume that $X$ follows a normal distribution with mean 8 and standard deviation 1.6.\\
Let $Y$ be the random variable that, for each bottle randomly selected from the daily production of source B, associates the calcium level it contains. We assume that $Y$ follows a normal distribution with mean 9 and standard deviation $\sigma$.

\begin{enumerate}
  \item Determine the probability that the calcium level measured in a bottle randomly taken from the daily production of source A is between $6.4 \mathrm { mg }$ and $9.6 \mathrm { mg }$.
  \item Calculate the probability $p ( X \leqslant 6.5 )$.
  \item Determine $\sigma$ knowing that the probability that a bottle randomly selected from the daily production of source B contains water that is very low in calcium is 0.1.
\end{enumerate}