Charlie is training for three events: a $$\(1500 \mathrm{~m}\)$$ swim, a $$\(40 \mathrm{~km}\)$$ bike ride and a $$\(10 \mathrm{~km}\)$$ run. From past experience his times, in minutes, for each of the three events independently have the following distributions. $$\(S \sim \mathrm{N}\left(41,5.2^{2}\right)\)$$ represents the time for the swim $$\(B \sim \mathrm{N}\left(81,4.2^{2}\right)\)$$ represents the time for the bike ride $$\(R \sim \mathrm{N}\left(57,6.6^{2}\right)\)$$ represents the time for the run find the value of $$\(t\)$$ (3) A triathlon consists of a $$\(1500 \mathrm{~m}\)$$ swim, immediately followed by a $$\(40 \mathrm{~km}\)$$ bike ride, immediately followed by a $$\(10 \mathrm{~km}\)$$ run. Charlie uses the answer to part (a) to find the probability that, in 6 successive independent triathlons, his time will exceed 3 hours on at least one occasion.

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