- The random variable \(A\) is defined as
$$A = B + 4 C - 3 D$$
where \(B\), \(C\) and \(D\) are independent random variables with
$$B \sim \mathrm {~N} \left( 6,2 ^ { 2 } \right) \quad C \sim \mathrm {~N} \left( 7,3 ^ { 2 } \right) \quad D \sim \mathrm {~N} \left( 4,1.5 ^ { 2 } \right)$$
Find \(\mathrm { P } ( A < 45 )\)