6 The numbers of barrels of oil, in millions, extracted per day in two oil fields $A$ and $B$ are modelled by the independent random variables $X$ and $Y$ respectively, where $X \sim \mathrm {~N} \left( 3.2,0.4 ^ { 2 } \right)$ and $Y \sim \mathrm {~N} \left( 4.3,0.6 ^ { 2 } \right)$. The income generated by the oil from the two fields is $\$ 90$ per barrel for $A$ and $\$ 95$ per barrel for $B$.\\
(i) Find the mean and variance of the daily income, in millions of dollars, generated by field $A$. [3]\\

(ii) Find the probability that the total income produced by the two fields in a day is at least $\$ 670$ million.\\

\hfill \mbox{\textit{CAIE S2 2017 Q6 [3]}}