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 answer Charlie should obtain. (3) Jane says that Charlie should not have used the answer to part (a) for the calculation in part (d).

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