A few flaws...
First of all, in a zombie holocaust, if you plan to continually sacrifice your friends, then you're good as dead. You will not survive alone. You will go insane, or you will die. If you're running from zombies, and you're friend trips, you should have time to pull them up, unless you're dumb enough to let the zombies get that close to you in the first place. Zombies (if there were Zombies) would more than likely move slow. A Shotgun is a great choice, there bigger then rifle ammo, but thats it, unless you're using long shelled slug ammo. Mp5 is hard to manage and is... an automatic, horrible for zombies, not accurate therefor ammo/weight/kill ratio is not at all better than the shotgun. In fact, the bullet is only around 20 grams lighter than a shotgun shell. thats 15 rounds per clip, and unless you have multiple clips, you'll have to reload the clips which takes a hell of a long time. If you do have multiple clips..... WAAY heavier than an adequate amount of shotgun shells. So you're good there, but a katana, assuming its battle ready, its good for medium defense. But if you can't go through a live willow branch (and a fairly thick one at that), you wont be able to use it effectively. And if the zombie gets the jump on you (one or two alone could surprise you), as in close enough to touch, you can't use the katana at all, not effectively on a dime and so close. not enough power or leverage. A better choice if you could only have one would be a crowbar. Its close range, good for 'oh shit' conditions, tough, good power behind it, vary good bludgeoning weapon, and can do more than just kill zombie, it can pry open doors, break windows, and do a large number of things you would find useful when adventuring around town.
So, thats it. If you don't agree, look it up, USE a katana, crowbar, Mp5 and shotgun THEN come back and disagree.
Good quiz, only saw a couple things wrong, but i liked it.