15 Jim Longlegs is an athlete whose specialist event is the triple jump. This is made up of a hop, a step and a jump. Over a season the lengths of the hop, step and jump sections, denoted by H, S and J respectively, are measured, from which the following models are proposed: H~ N(5.5, 0.5?) s~ N(5.1, 0.6²) J~N(6.2, 0.8²) where all distances are in metres. Assume that H, S and J are independent. (i) In what proportion of his triple jumps will Jim's total distance exceed 18 metres? (ii) In six successive independent attempts, what is the probability that at least one total distance will exceed 18 m? (iii) What total distance will Jim exceed 95% of the time?

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