6 An aircraft, based at airport A, flies regularly to and from airport B.
The aircraft's flying time, \(X\) minutes, from A to B has a mean of 128 and a variance of 50 .
The aircraft's flying time, \(Y\) minutes, on the return flight from B to A is such that $$\mathrm { E } ( Y ) = 112 , \quad \operatorname { Var } ( Y ) = 50 \quad \text { and } \quad \rho _ { X Y } = - 0.4$$

1. Given that \(F = X + Y\) :
   1. find the mean of \(F\);
   2. show that the variance of \(F\) is 60 .
2. At airport B , the stopover time, \(S\) minutes, is independent of \(F\) and has a mean of 75 and a variance of 36 . Find values for the mean and the variance of:
   1. \(T = F + S\);
   2. \(M = F - 3 S\).
3. Hence, assuming that \(T\) and \(M\) are normally distributed, determine the probability that, on a particular round trip of the aircraft from A to B and back to A :
   1. the time from leaving A to returning to A exceeds 300 minutes;
   2. the stopover time is greater than one third of the total flying time.