Natalie Wood was one of her closest friends. When Norma became ill with cancer Wood reportedly paid the medical bills as well as the (eventual) funeral costs.
Studied drama at Texas State College for Women (known as Texas Woman's University (TWU) since 1957), in Denton, Texas.
The daughter of Sam Zuckerman of Texas, Norma was raised by her aunt, Helen (Hartzband) Zuckerman of New York after Norma's mother died in childbirth.