6 The distance, \(X\) metres, between successive breaks in a water pipe is modelled by an exponential distribution. The mean of \(X\) is 25
The distance between two successive breaks is measured. A water pipe is given a 'Red' rating if the distance is less than \(d\) metres.
The government has introduced a new law changing \(d\) to 2
Before the government introduced the new law, the probability that a water pipe is given a 'Red' rating was 0.05
6
- Explain whether or not the probability that a water pipe is given a 'Red' rating has increased as a result of the new law.
6 - Find the probability density function of the random variable \(X\).
6
- After investigation, the distances between successive breaks in water pipes are found to have a standard deviation of 5 metres.
Explain whether or not the use of an exponential model in parts (a) and (b) is appropriate.
[0pt]
[2 marks]