\textbf{Part A - Waiting time}

\begin{enumerate}
  \item In this question, we are interested in the waiting time of an Internet customer when they contact the telephone assistance before reaching an operator. A study makes it possible to model this waiting time in minutes by the random variable $D_1$ which follows the exponential distribution with parameter 0.6.\\
a. What is the average waiting time that an Internet customer calling this assistance line can expect?\\
b. Calculate the probability that the waiting time of a randomly chosen Internet customer is less than 5 minutes.
  \item In this question, we are interested in the waiting time of a mobile customer when they contact the telephone assistance before reaching an operator. We model this waiting time in minutes by the random variable $D_2$ which follows an exponential distribution with parameter $\lambda$, $\lambda$ being a strictly positive real number.\\
a. Given that $P\left(D_2 \leqslant 4\right) = 0.798$, determine the value of $\lambda$.\\
b. Taking $\lambda = 0.4$, can we consider that fewer than $10\%$ of randomly chosen mobile customers wait more than 5 minutes before reaching an operator?
\end{enumerate}