Additionally, if the sin was committed by a priest (I Peter 4:17) or by the nation then the animal had to be a young bull. If the sin was committed by a leader of the people then he was to offer a young male goat. If one of the common people sinned then they were supposed to offer a young female goat or lamb and the blood was only placed on the horns of the brazen altar (and poured at the foot of the same altar) ... none of it was taken into the Tabernacle.
The most significant part of this whole process was the promise that their sin would be forgiven. If there had been no promise of forgiveness, what good would all of this do? Of course, we know that the forgiveness was incomplete. The sin sacrifice had to be repeated and the sins were not ultimately taken away (Hebrews 10:4-6). God's mercy was applied but His justice was only temporarily appeased. Only the blood of Christ makes full propitiation for sins and only His blood can cure our moral disease (Hebrews 9:14). Only Jesus' blood provides for a new birth and a new nature.
One final thing... the bodies of the sin offerings were burned on the outside of the camp (Hebrews 13:11-13). As the personification of sin (II Corinthians 5:21) Jesus was rejected, cast out and relegated to the outside.