3 The number of minutes, \(X\), for which a particular model of laptop computer will run on battery power is Normally distributed with mean 115.3 and standard deviation 21.9.

1. (A) Find \(\mathrm { P } ( X < 120 )\).
   (B) Find \(\mathrm { P } ( 100 < X < 110 )\).
   (C) Find the value of \(k\) for which \(\mathrm { P } ( X > k ) = 0.9\). The number of minutes, \(Y\), for which a different model of laptop computer will run on battery power is known to be Normally distributed with mean \(\mu\) and standard deviation \(\sigma\).
2. Given that \(\mathrm { P } ( Y < 180 ) = 0.7\) and \(\mathrm { P } ( Y < 140 ) = 0.15\), find the values of \(\mu\) and \(\sigma\).
3. Find values of \(a\) and \(b\) for which \(\mathrm { P } ( a < Y < b ) = 0.95\).