Recover a component normal distribution from a sum of two observations

$X\sim N(20,\sigma^2)$.

(i) Given $P(12<X<k)=P(X>k)=0.42065$, show that σ=8 to the nearest whole number, and find k.4 marks

$X=Y_1+Y_2-4$, where $Y_1,Y_2$ are independent observations of a normal variable Y. W is independent of Y and has normal mean 25 and variance 16.

(ii) Using σ=8, find $E(Y)$ and $\operatorname{Var}(Y)$, then $P(W>2Y)$.5 marks