3 In the manufacture of fibre optical cable (FOC), flaws occur randomly. Whether any point on a cable is flawed is independent of whether any other point is flawed. The number of flaws in 100 m of FOC of standard diameter is denoted by \(X\).
- State a further assumption needed for \(X\) to be well modelled by a Poisson distribution.
Assume now that \(X\) can be well modelled by the distribution \(\operatorname { Po } ( 0.7 )\).
- Find the probability that in 300 m of FOC of standard diameter there are exactly 3 flaws.
The number of flaws in 100 m of FOC of a larger diameter has the distribution \(\mathrm { Po } ( 1.6 )\).
- Find the probability that in 200 m of FOC of standard diameter and 100 m of FOC of the larger diameter the total number of flaws is at least 4.