During the fifteen days preceding the start of the university term, the telephone switchboard of a student mutual aid organisation records a record number of calls.\\
Callers are first placed on hold and hear background music and a pre-recorded message.\\
During this first phase, the waiting time, expressed in seconds, is modelled by the random variable $X$ which follows the exponential distribution with parameter $\lambda = 0{,}02 \mathrm{~s}^{-1}$.\\
Callers are then connected with a customer service representative who answers their questions. The exchange time, expressed in seconds, during this second phase is modelled by the random variable $Y$, expressed in seconds, which follows the normal distribution with mean $\mu = 96$ s and standard deviation $\sigma = 26 \mathrm{~s}$.

\begin{enumerate}
  \item What is the average total duration of a call to the telephone switchboard (waiting time and exchange time with the customer service representative)?
  \item A student is chosen at random from among the callers to the telephone switchboard.\\
a. Calculate the probability that the student is placed on hold for more than 2 minutes.\\
b. Calculate the probability that the exchange time with the adviser is less than 90 seconds.
  \item A female student, chosen at random from among the callers, has been waiting for more than one minute to be connected with the customer service. Tired, she hangs up and dials the number again. She hopes to wait less than thirty seconds this time.\\
Does hanging up and calling back increase her chances of limiting the additional waiting time to 30 seconds, or would she have been better off staying on the line?
\end{enumerate}