Write an inequality to describe the region.

The solid upper hemisphere of the sphere of radius $2$ centered at the origin.

$z0,x^2{y}^2{z}^{2}4$

$z0,x^2{y}^2{z}^{2}4$

$z0,x^2{y}^2{z}^{2}4$

$z0,\sqrt[\phantom{2}]{x^2{y}^2{z}^2}4$

none of these