3 The continuous random variable \(T\) has mean \(\mu\) and standard deviation \(\sigma\). It is known that \(\mathrm { P } ( T < 140 ) = 0.01\) and \(\mathrm { P } ( T < 300 ) = 0.8\).
- Assuming that \(T\) is normally distributed, calculate the values of \(\mu\) and \(\sigma\).
In fact, \(T\) represents the time, in minutes, taken by a randomly chosen runner in a public marathon, in which about \(10 \%\) of runners took longer than 400 minutes.
- State with a reason whether the mean of \(T\) would be higher than, equal to, or lower than the value calculated in part (i).