Tell Me Bozo Did Not Do It

Yesterday, circus owner P.U. Burnem gathered his clowns, and told them he was going to fire every one of them after that night's performance. Last night, Burnem's electrocuted body was found underneath a bumper car. The following facts have been determined; can you find the killer?

1. All male clowns with rubber noses wear red wigs.
2. None of the juggling clowns wear both a red wig and a rubber nose.
3. All happy clowns without rubber noses are part of the "tiny car" act.
4. None of the sad clowns without rubber noses wear red wigs.
5. All of the men who are sad clowns wear rubber noses.
6. None of the happy clowns who can't juggle wear red wigs.
7. All clowns with rubber noses who can't juggle are in the "tiny car" act.

The coroner was able to put the time of death at 8:17, which was during the clowns' "tiny car" act. Therefore, nobody involved in that act could possibly be the killer.

The list of suspects has been narrowed to the following four clowns. Which one of them bumped off the circus owner?

1. Alberto, who can juggle
2. Babs, who wears a red wig
3. Crazy Chester, who has a rubber nose
4. Doris, who is a happy clown