5. 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 govemment has introduced a new law changing \(d\) to 2
Before the govermment introduced the new law, the probability that a water pipe is given a 'Red' rating was 0.05

1. Explain whether or not the probability that a water pipe is given a 'Red' rating has increased as a result of the new law.
2. Find the probability density function of the random variable \(X\).
3. 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]