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)
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Dupe of MC-32575
confirmed in pre3 aswell