5 The times, in months, taken by a builder to build two types of house, $P$ and $Q$, are represented by the independent variables $T _ { 1 } \sim \mathrm {~N} \left( 2.2,0.4 ^ { 2 } \right)$ and $T _ { 2 } \sim \mathrm {~N} \left( 2.8,0.5 ^ { 2 } \right)$ respectively.\\
(i) Find the probability that the total time taken to build one house of each type is less than 6 months.\\

(ii) Find the probability that the time taken to build a type $Q$ house is more than 1.2 times the time taken to build a type $P$ house.\\

\hfill \mbox{\textit{CAIE S2 2018 Q5}}