Math Help - bivariate normal distribution

1. bivariate normal distribution

if $X,Y \sim BVN$ AND : $\mu \scriptscriptstyle {x} =-3$ $\sigma \scriptscriptstyle {x} =5$ $\mu \scriptscriptstyle {y} =10$ $\sigma \scriptscriptstyle {y} = 3$ $\rho =\frac{3}{5}$ how i can find : $p(-5\prec x \prec 5)$ ???????

2. Hello,
Originally Posted by flower3
if $X,Y \sim BVN$ AND : $\mu \scriptscriptstyle {x} =-3$ $\sigma \scriptscriptstyle {x} =5$ $\mu \scriptscriptstyle {y} =10$ $\sigma \scriptscriptstyle {y} = 3$ $\rho =\frac{3}{5}$ how i can find : $p(-5\prec x \prec 5)$ ???????
If (X,Y) follows a bivariate normal distribution, then in particular, X follows a normal distribution.
Its mean is -3 and its variance is 5^2=25.
$X\sim\mathcal{N}(-3,25)$
--> $\frac{X+3}{5}\sim\mathcal{N}(0,1)$
$\mathbb{P}(-5