Identify the elements from their atomic numbers

• $X$ has atomic number $33$ $\Rightarrow$ element is As (Arsenic)
• $Y$ has atomic number $53$ $\Rightarrow$ element is I (Iodine)
• $Z$ has atomic number $83$ $\Rightarrow$ element is Bi (Bismuth)

Classify each element

• Arsenic (As): It is a metalloid.
• Iodine (I): It is a non-metal (halogen).
• Bismuth (Bi): It is a metal.

Match with the options

• A: $X$ and $Y$ are metalloids and $Z$ is a metal.
  This is incorrect because iodine is not a metalloid; it is a non-metal.

• B: $X$ and $Z$ are non-metals and $Y$ is a metalloid.
  This is incorrect because arsenic is a metalloid, bismuth is a metal, and iodine is a non-metal.

• C: $X$ is a metalloid, $Y$ is a non-metal and $Z$ is a metal.
  This matches exactly.

• D: $X$, $Y$ and $Z$ are metals.
  Incorrect.

Final answer

Therefore, the correct option is: $\boxed{\text{C}}$

Comparison with stored correct answer

Stored correct answer = C.
My derived answer = C.
Hence, they agree.