6 Alyssa lives in the country but works in a city centre.
Her journey to work each morning involves a car journey, a walk and wait, a train journey, and a walk. Her car journey time, \(U\) minutes, from home to the village car park has a mean of 13 and a standard deviation of 3 . Her time, \(V\) minutes, to walk from the village car park to the village railway station and wait for a train to depart has a mean of 15 and a standard deviation of 6 . Her train journey time, \(W\) minutes, from the village railway station to the city centre railway station has a mean of 24 and a standard deviation of 4 . Her time, \(X\) minutes, to walk from the city centre railway station to her office has a mean of 9 and a standard deviation of 2 . The values of the product moment correlation coefficient for the above 4 variables are $$\rho _ { U V } = - 0.6 \quad \text { and } \quad \rho _ { U W } = \rho _ { U X } = \rho _ { V W } = \rho _ { V X } = \rho _ { W X } = 0$$

1. Determine values for the mean and the variance of:
   1. \(M = U + V\);
   2. \(D = W - 2 U\);
   3. \(T = M + W + X\), given that \(\rho _ { M W } = \rho _ { M X } = 0\).
2. Assuming that the variables \(M , D\) and \(T\) are normally distributed, determine the probability that, on a particular morning:
   1. Alyssa's journey time from leaving home to leaving the village railway station is exactly 30 minutes;
   2. Alyssa's train journey time is more than twice her car journey time;
   3. Alyssa's total journey time is between 50 minutes and 70 minutes.