Charlie is training for three events: a $$\(1500 \mathrm{~m}\)$$ swim, a $$\(40 \mathrm{~km}\)$$ bike ride and a $$\(10 \mathrm{~km}\)$$ run. From past experience his times, in minutes, for each of the three events independently have the following distributions. $$\(S \sim \mathrm{N}\left(41,5.2^{2}\right)\)$$ represents the time for the swim $$\(B \sim \mathrm{N}\left(81,4.2^{2}\right)\)$$ represents the time for the bike ride $$\(R \sim \mathrm{N}\left(57,6.6^{2}\right)\)$$ represents the time for the run Find the probability that the time for a randomly selected swim will be at least 20 minutes quicker than the time for a randomly selected run. (4) Given that $$\(\mathrm{P}(S+B+R> t)=0.95\)$$

Answer:

Knowledge points:

Solution: