Using the command(with command blocks):
/summon Zombie ~ ~1 ~ {Invulnerable:1,PresistenceRequired:1,ActiveEffects:[3:

{Id:2,Duration:32768,Amplifier:14}

,1:

{Id:14,Duration:32768,Amplifier:1}

],Silent:1}

does apply invisibility but not slowness, the slowness gets applied if the speed is updated with a trown potion (aka splash potion of speed/slowness)