1 A radar device is used to detect flaws in motorway roads before they become dangerous. The number of flaws in a 1 km stretch of motorway is denoted by \(X\). It may be assumed that flaws occur randomly.
- State two further assumptions that are necessary for \(X\) to be well modelled by a Poisson distribution.
Assume now that \(X\) can be modelled by distribution \(\operatorname { Po } ( 5.7 )\).
- Determine the probability that in a randomly chosen stretch of motorway, of length 1 km , there are between 8 and 11 flaws, inclusive.
- Determine the probability that in two randomly chosen, non-overlapping, stretches of motorway, each of length 5 km , there are at least 30 flaws in one stretch and fewer than 30 flaws in the other stretch.