You Do Need power plug adapter while traveling from Central African Republic to Norfolk Island.

Here is Why You Need An Adapter

The outlet and plug type used in Norfolk Island is I and in Central African Republic are C and E. This is how they look like.

Central African Republic

In Central African Republic, outlets of type C and E are in use.

Type C

Type E

Norfolk Island

In Norfolk Island, outlets of type I are in use.

Type I