During a lunchtime tryst in Phoenix, Arizona, a real estate secretary named Marion Crane discusses with her boyfriend, Sam Loomis, how they cannot afford to get married because of Sam's debts. After lunch, Marion returns to work, where a client drops off a $40,000 cash payment on a property. Her boss asks her to deposit the money in the bank, and she asks if she can take the rest of the afternoon off. Returning home, she begins to pack for an unplanned trip, deciding to steal the money and give it to Sam in Fairvale, California. She is seen by her boss on her way out of town, which makes her nervous. During the trip, she pulls over on the side of the road and falls asleep, only to be awakened by a state patrol officer. He is suspicious about her nervous behavior but allows her to drive on. Shaken by the encounter, Marion stops at an automobile dealership and trades in her Ford Mainline, with its Arizona license plates, for a Ford Custom 300 that has California tags. Her transaction is all for naughtâthe highway patrolman sees her at the car dealership and witnesses her purchase of the newer car.
Driving on, Marion encounters a sudden rainstorm and decides to stop for the night at the Bates Motel; the proprietor, Norman Bates, invites her to a light dinner after she checks in. She accepts, but then hears an argument between Norman and his mother about bringing a woman into her house. They eat in the motel parlor, where he tells her about his hobby of taxidermy and his life with his mother, who is mentally ill and forbids him to have a life outside of her. Returning to her room, Marion decides to go back to Phoenix to return the stolen money. She prepares to take a shower, unaware that Norman is spying on her. As she is showering, a shadowy female figure suddenly comes in and stabs her to death with a chef's knife. Norman discovers the murder and meticulously cleans up the crime scene, putting Marion's corpse and her possessionsâincluding the embezzled moneyâinto the trunk of her car and sinking it in the swamps near the motel.
A week later, Marion's sister Lila arrives in Fairvale and confronts Sam about the whereabouts of her sister. A private investigator named Arbogast approaches them and confirms that Marion is wanted for stealing the $40,000 from her employer. He eventually comes across the Bates Motel, where Norman's behavior arouses his suspicions. After hearing that Marion had met with Norman's mother, he asks to speak with her, but Norman refuses. Arbogast calls Lila and Sam, informing them of what he has discovered and saying he intends to speak with Norman's mother. He goes to the Bates' home in search of her; as he reaches the top of the stairs, Mrs. Bates suddenly appears from the bedroom and murders him. When Lila and Sam do not hear from Arbogast, they go to the local sheriff, who informs them that Mrs. Bates has been dead for ten years; she had killed herself and her lover. Concerned, Lila and Sam make their way to the motel. Norman takes his unwilling mother from her room, telling her he needs to hide her for a while in the fruit cellar.
At the motel, Lila and Sam meet Norman. Sam distracts him by striking up a conversation while Lila sneaks up to the house. When Norman eventually realizes what they want, he knocks Sam out and rushes to the house. Lila sees Norman approaching and attempts to hide by going down steps that lead to a cellar. There she finds Mrs. Bates sitting in a chair. Lila turns her around and discovers that she is in fact a mummified corpse. Lila screams as a figure comes running into the cellar: Norman, holding a chef's knife and wearing his mother's clothes and a wig. Before Norman can attack Lila, Sam, having regained consciousness, subdues him.
At the local courthouse, a psychiatrist explains that Norman murdered Mrs. Bates and her lover 10 years prior out of jealousy. Unable to bear the guilt, he exhumed her corpse and began to treat it as if she were still alive. In order to preserve that illusion, he recreated his mother in his own mind as an alternate personality, often dressing in her clothes and talking to himself in her voice. The "Mother" personality is as jealous and possessive as the real Mrs. Bates had been: Whenever Norman feels attracted to another woman, "Mother" flies into a rage and kills her. As "Mother", Norman had killed two missing girls prior to Marion, as well as Arbogast. The psychiatrist then says the "Mother" personality has taken permanent hold of Norman's mind. While Norman sits in a holding cell, Mrs. Bates' voice is heard protesting that the murders were Norman's doing and that she "wouldn't even harm a fly." Meanwhile, Marion's car is pulled out of the swamp.

Question: Who appears to have murdered the private investigator? 
Answer: Mrs. Bates
Alternative answer: "Mother" Norman did