A random variable $x$ is normally distributed with a mean of $100$ and a variance of $100,$ and a random variable $Y$ is normally distributed with a mean of $170$ and a variance of $289.$ The random variables have a correlation coefficient equal to $0\mathrm{.}5.$ Find the mean and variance of the random variable below.

$W=8x+5Y$

${}_W=$

$($Do not round.$)$

${}_W^2=$

$($Do not round.$)$