Importance sampling estimate

Question

Suppose that one is interested in estimating the tail probability $$ P(Z \ge b) $$ for $$Z \sim N(0,1)$$ and a large threshold b. What is the expression for the importance sampling estimate with the alternative sampling distribution $$ N(\theta, 1) . $$ My answer: $$ P(Z \ge b) = E_f[h(X)] $$ $$ f(x) = \frac{1}{\sqrt(2\pi)} e^{-0.5x^2} $$ $$ g(x) = \frac{1}{\sqrt(2\pi)} e^{-0.5(x-b)^2} $$ $$\frac{f}{g} = e^{0.5b^2 - bx} $$ important sampling estimate = $$\mu = E_g[h(Y)e^{-0.5(y-b)^2}]$$ $$\mu = E_g[1_{Y >= b}e^{-0.5(y-b)^2}]$$ Is this correct ?