7．（i）As part of a recruitment exercise candidates are required to complete three separate tasks．The times taken，\(A , B\) and \(C\) ，in minutes，for candidates to complete the three tasks are such that $$A \sim \mathrm {~N} \left( 21,2 ^ { 2 } \right) , B \sim \mathrm {~N} \left( 32,7 ^ { 2 } \right) \text { and } C \sim \mathrm {~N} \left( 45,9 ^ { 2 } \right)$$ The time taken by an individual candidate to complete each task is assumed to be independent of the time taken to complete each of the other tasks． A candidate is selected at random．
（a）Find the probability that the candidate takes a total time of more than 90 minutes to complete all three tasks．
（b）Find \(\mathrm { P } ( A > B )\)
（ii）A simple random sample，\(X _ { 1 } , X _ { 2 } , X _ { 3 } , X _ { 4 }\) ，is taken from a normal population with mean \(\mu\) and standard deviation \(\sigma\) Given that $$\bar { X } = \frac { X _ { 1 } + X _ { 2 } + X _ { 3 } + X _ { 4 } } { 4 }$$ and that $$\mathrm { P } \left( X _ { 1 } > \bar { X } + k \sigma \right) = 0.1$$ where \(k\) is a constant，
find the value of \(k\) ，giving your answer correct to 3 significant figures．