7 The waiting time, \(T\) minutes, before a customer is served in a restaurant has distribution function F given by
$$\mathrm { F } ( t ) = \begin{cases} 1 - \mathrm { e } ^ { - \lambda t } & t \geqslant 0
0 & t < 0 \end{cases}$$
where \(\lambda\) is a positive constant. The standard deviation of \(T\) is 8 . Find
- the value of \(\lambda\),
- the probability that a customer has to wait between 5 and 10 minutes before being served,
- the median value of \(T\).