The attack was reported just after 7 a.m. Sunday in the 16000 block of Crenshaw Boulevard, according to the Los Angeles County Sheriff's Department. Authorities said the victim was collecting recyclables at the campus when she was assaulted.
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The woman was taken to a hospital, where she died the next day. She was described as an Asian woman between the ages of 60 and 65. Her name has not been released.
An investigation by the El Camino College Police Department and Sheriff's Homicide Bureau led to the arrest of Jeffery Davis near the campus, authorities said.
Police reviewed campus security footage and say they recognized Davis. They say they have had run-ins with him before and believe he is homeless.
They went to a nearby park and arrested him in connection with the assault.
It was unclear what motivated the assault or if the suspect knew the victim.
The Los Angeles County Department of Medical Examiner will determine the victim's cause of death.
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Most of the campus is empty since school is out for winter break.
El Camino College student Nicholas Scott Flores said police are at the campus often and is surprised by the brutal attack.
Anyone with information regarding the killing is asked to call the Sheriff's Homicide Bureau at 323-890-5500. Tipsters who prefer to remain anonymous can call Crime Stoppers at 800-222-8477.
City News Service contributed to this report.