A factory of frozen desserts has an automated line to fill ice cream cones. Ice cream cones are packaged individually and then packaged in batches of 2000 for wholesale sale. It is considered that the probability that a cone has any defect before its packaging in bulk is equal to 0.003. We denote by $X$ the random variable which, to each batch of 2000 cones randomly selected from production, associates the number of defective cones present in this batch. It is assumed that the production is large enough that the draws can be assumed to be independent of each other.

\begin{enumerate}
  \item What is the distribution followed by $X$? Justify the answer and specify the parameters of this distribution.
  \item If a customer receives a batch containing at least 12 defective cones, the company then proceeds to exchange it.\\
Determine the probability that a batch is not exchanged; the result will be rounded to the nearest thousandth.
\end{enumerate}