6. The time, in minutes, taken by men to run a marathon is modelled by a normal distribution with mean 240 minutes and standard deviation 40 minutes.
- Find the proportion of men that take longer than 300 minutes to run a marathon.
(3)
Nathaniel is preparing to run a marathon. He aims to finish in the first 20\% of male runners. - Using the above model estimate the longest time that Nathaniel can take to run the marathon and achieve his aim.
(3)
The time, \(W\) minutes, taken by women to run a marathon is modelled by a normal distribution with mean \(\mu\) minutes.
Given that \(\mathrm { P } ( W < \mu + 30 ) = 0.82\) - find \(\mathrm { P } ( W < \mu - 30 \mid W < \mu )\)