Concept:
Specific gravity is the ratio of the density of a substance to the density of water at a standard temperature.
Step 1: Alumina is aluminium oxide:
\[
Al_2O_3
\]
Step 2: Alumina is a dense ceramic oxide with high hardness, high melting point, and good chemical stability.
Step 3: The specific gravity of alumina is approximately:
\[
3.9 \text{ to } 4.0
\]
Step 4: Among the given options, the nearest and correct value is:
\[
4.0
\]
Therefore, the correct answer is:
\[
\boxed{4.0}
\]