Alex: Excuse me for being a good citizen.
Alice: You got hit with a book?
Earl Unger: Books. Plural a trunk, full of books. Then a set of weights. We got hit twice, you dumb broad.
Stan: Hey, Alex, could you pass me the false alarms? I mean, the peas.
Alex: Mrs. Hess did you ever have the chikenpox?
Mrs. Hess: I had the chicken pox when Herbert Hoover was in the White House.
Mrs. Hess: Well what do you want a wilkie button?
Alice: Good Afternoon, my husband and I just moved into the neighborhood.
Peter Beaupre: We are going to Chicago.
Earl Unger: In the winter? I packed tropical.
Answer: It was Jernigan who thought there was a woman in the shower and he couldn't take the risk that if it was a woman, that she would eventually get out and see intruders in the house and call for the police. The only option open to Jernigan would be to kill her so there'd be no witnesses.
No it was Beaupre who thought there was a woman in the house.
I've seen the movie and I can confirm that it was Jernigan who opened the shower curtain because he thought a woman was in the shower.