After she finished high school, she began working in retail sales for a Saks Fifth Avenue store in Detroit.

[4] Randolph originally portrayed Trixie in skits on The Jackie Gleason Show and The Honeymooners, which included Jackie Gleason as Ralph Kramden, Art Carney as Ed Norton, Audrey Meadows as Alice Kramden, and Randolph as Thelma "Trixie" Norton.

Randolph talked about a hectic workload for filming the show, with getting all 39 episodes shot within a calendar year.

[10] Randolph was typecast after leaving The Jackie Gleason Show and seldom found other acting roles.

'"[11] She performed in summer stock musicals, made commercials, and had a few guest appearances on television shows, including her reprisal of Trixie Norton (along with Audrey Meadows reprising her role as Alice Kramden) in the 1991 episode "Fur Flies" in Hi Honey, I'm Home!.

[6] She died of natural causes at age 99 at home in Manhattan's Upper West Side on January 13, 2024.