Correlation from a conditional interval

Let $(X,Y)$ be a random vector having the bivariate normal distribution with $E(X)=2$, $E(Y)=10$, $\operatorname{Var}(X)=9$, $\operatorname{Var}(Y)=25$, and the correlation coefficient between $X$ and $Y$ equals $\rho>0$. If $P(4<Y<16\mid X=2)=0.8664$, then $\rho$ equals __________ (rounded off to two decimal places) [You may use $\Phi(1.5)=0.9332$, $\Phi(2)=0.9772$]