Step 1: List the three premises clearly.
We are told (a) All Zs are Ys, (b) No Y is an X, and (c) Every X is a W. Our job is to test which conclusions are forced by these.
Step 2: Picture the sets with circles.
Draw a big circle $Y$. Since all Zs are Ys, the $Z$ circle sits fully inside $Y$, so $Z \subseteq Y$. Since no Y is an X, the $X$ circle lies completely outside $Y$, with no overlap.
Step 3: Place W using premise (c).
Every X is a W means the $X$ circle sits inside a larger $W$ circle. But notice: the premises tell us nothing about where $Z$ (or $Y$) stands relative to $W$.
Step 4: Test Conclusion II - Zs are not Xs.
$Z$ lives inside $Y$, and $X$ is entirely outside $Y$. Two regions that never touch cannot share a member, so no $Z$ can be an $X$. Conclusion II is forced and true.
Step 5: Test Conclusion I - Some Ws are Zs.
The only thing linking $W$ to anything is that it contains $X$. There is no stated bridge between $W$ and $Z$. We could draw $W$ far from the $Y$-$Z$ block entirely, giving zero overlap with $Z$. Since a valid arrangement exists where no W is a Z, Conclusion I is not guaranteed.
Step 6: Combine the verdicts.
Conclusion II always holds; Conclusion I only sometimes holds, so it does not follow. Hence only Conclusion II follows, matching option 3.
\[ \boxed{\text{Only conclusion II follows}} \]