5 The distance, \(X \mathrm {~km}\), completed by a new car before any mechanical fault occurs has distribution function F given by
$$\mathrm { F } ( x ) = \begin{cases} 1 - \mathrm { e } ^ { - a x } & x \geqslant 0
0 & \text { otherwise } \end{cases}$$
where \(a\) is a positive constant. The mean value of \(X\) is 10000 . Find
- the value of \(a\),
- the probability that a new car completes less than 15000 km before any mechanical fault occurs.
The probability that a new car completes at least \(d \mathrm {~km}\) before any mechanical fault occurs is 0.75 .
- Find the value of \(d\).