- Charlie is training for three events: a 1500 m swim, a 40 km bike ride and a 10 km run.
From past experience his times, in minutes, for each of the three events independently have the following distributions.
$$\begin{aligned}
& S \sim \mathrm {~N} \left( 41,5.2 ^ { 2 } \right) \text { represents the time for the swim }
& B \sim \mathrm {~N} \left( 81,4.2 ^ { 2 } \right) \text { represents the time for the bike ride }
& R \sim \mathrm {~N} \left( 57,6.6 ^ { 2 } \right) \text { represents the time for the run }
\end{aligned}$$
- Find the probability that Charlie's total time for a randomly selected swim, bike ride and run exceeds 3 hours.
- 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.
Given that \(\mathrm { P } ( S + B + R > t ) = 0.95\)
- find the value of \(t\)
A triathlon consists of a 1500 m swim, immediately followed by a 40 km bike ride, immediately followed by a 10 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.
- Find the answer Charlie should obtain.
Jane says that Charlie should not have used the answer to part (a) for the calculation in part (d).
- Explain whether or not Jane is correct.