Randolph was born in Detroit, Michigan. As a teenager, she acted with the Wayne University Workshop. After she finished high school, she began working in retail sales for a Saks Fifth Avenue store in Detroit. When a touring company of Stage Door played in Detroit, she auditioned, got a part, and performed for the rest of the tour. She moved to New York City in 1943 to pursue an acting career. She took roles on Broadway and landed various television roles.
In 1951, she was seen in a Clorets commercial by Jackie Gleason and was asked to appear in a skit on Cavalcade of Stars, Gleason's variety show on the DuMont Television Network. Soon after, she was cast as Trixie in The Honeymooners. Several New York columnists referred to her as the "Garbo of Detroit". "That's still a mystery ... I was a nobody in Detroit. Why Garbo? Well, she was Scandinavian — and so was I", responded Randolph.
Randolph is the last surviving member of the Honeymooners quartet, which included Jackie Gleason as Ralph Kramden, Art Carney as Ed Norton, Audrey Meadows as Alice Kramden, and Randolph as Thelma "Trixie" Norton.

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