Question 1034553
{{{E(Y) = mu[Y] = -2*0.11 + 0*0.32 + 3*0.57  = 1.49}}}.

Now {{{E(Y^2) = (-2)^2*0.11 + 0^2*0.32 + 3^2*0.57  = 5.57}}}

{{{(sigma)^2[Y] = E(Y^2) -  (mu[Y])^2 = 5.57 - 1.49^2 = 3.3499}}}

==> {{{sigma[Y] = sqrt(3.3499) = 1.83}}}, to three significant figures
 
{{{P(mu[Y] - 3*sigma[Y] < Y < mu[Y] + 3*sigma[Y]) = P(-4 < Y < 6.98) = 1}}}