2. A survey is carried out into the length of time for which customers wait for a response on a telephone helpline. A statistician who is analysing the results of the survey starts by modelling the waiting time, \(X\) minutes, by an exponential distribution with probability density function $$f ( x ) = \left\{ \begin{array} { c c } \lambda e ^ { - \lambda x } & x \geq 0
0 & x < 0 \end{array} \right.$$ The mean waiting time is found to be 5 minutes.
a. State the value of \(\lambda\).
b. Use the model to calculate the probability that a customer has to wait longer that 20 minutes for a response.