Question 503214
E(.)= the mean
s(.)= the standard deviation

So, E(X)=110 s(X)=18 ; E(Y)=215 s(Y)=30
    r(X,Y)=0.75
The standard deviation of X+Y, formula; 
 {{{Var(X+Y)= Var(x)+Var(y)+2cov(x,y)}}}  "Var= {{{s^2}}} "

The above formula comes from this general formula 
{{{Var(aX+bY)= a^2Var(x)+b^2Var(y)+2abcov(x,y)}}} note: a and b are equal to 1, the coefficient of X and Y

{{{Var(X+Y)= 18^2+30^2+2cov(x,y)}}}. We therefore need to find the covariance of X and Y
Formula: {{{r(x,y)= Cov(x,y)/(s(x)*s(y))}}} . The actual formula for finding the cov(x,y) is {{{E(XY)-E(X)*E(Y)}}}. We don't know the value of E(XY) so we use the alternative since r(x,y) is given.

{{{r(x,y)= Cov(x,y)/(s(x)*s(y))}}}
{{{0.75= Cov(x,y)/(18*30)}}}
{{{Cov(x,y)= 0.75*(18*30)}}}
Cov(x,y)=405

However, {{{Var(X+Y)= 18^2+30^2+2cov(x,y)}}}
         {{{Var(X+Y)= 18^2+30^2+2*405}}}
           {{{Var(X+Y)= 2034}}}
That implies {{{sqrt(2034)}}} is equal to the standard deviation of X+Y
So, s(X+Y)=45.10

I hope you really understand the steps. And your feedback will be appreciated.