Step 1: Recall income elasticity of demand.
Income elasticity of demand measures the responsiveness of quantity demanded to changes in consumer income.
\[
E_Y=\frac{\%\Delta Q}{\%\Delta Y}
\]
Step 2: Analyze Statement I.
For a normal good, demand increases when income increases.
Thus,
\[
E_Y>0
\]
Therefore, Statement I is correct.
Step 3: Analyze Statement II.
For an inferior good, demand decreases when income increases.
Thus,
\[
E_Y<0
\]
Therefore, Statement II is correct.
Step 4: Analyze Statement III.
Luxury goods have income elasticity greater than \(1\).
\[
E_Y>1
\]
Hence, Statement III is incorrect because it says elasticity is less than \(1\).
Step 5: Final conclusion.
Thus, Statements I and II are correct, but Statement III is not correct.
\[
\boxed{\text{Both I and II are CORRECT, but III is NOT CORRECT}}
\]
Hence, the correct option is (D).