In basketball, it is possible to score baskets worth one point, two points or three points.

The coach of a basketball team decides to study the success statistics of his players' shots. He observes that during training, when Victor attempts a three-point shot, he succeeds with a probability of 0.32.
During a training session, Victor makes a series of 15 three-point shots. We assume that these shots are independent.

Let $N$ be the random variable giving the number of baskets scored.
The results of the requested probabilities should be, if necessary, rounded to the nearest thousandth.

\begin{enumerate}
  \item We admit that the random variable $N$ follows a binomial distribution. Specify its parameters.
  \item Calculate the probability that Victor succeeds in exactly 4 baskets during this series.
  \item Determine the probability that Victor succeeds in at most 6 baskets during this series.
  \item Determine the expected value of the random variable $N$.
  \item Let $T$ be the random variable giving the number of points scored after this series of shots.\\
a. Express $T$ as a function of $N$.\\
b. Deduce the expected value of the random variable $T$. Give an interpretation of this value in the context of the exercise.\\
c. Calculate $P ( 12 \leqslant T \leqslant 18 )$.
\end{enumerate}