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.
''The Honeymooners''
As of 2020, Randolph was the only 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. Randolph was not the first "Trixie Norton"; Elaine Stritch appeared as a burlesque "Trixie" in 1951 in Cavalcade of Stars, where the premise for The Honeymooners first began. Stritch played the role only once and then Randolph took over. Randolph had met her future Honeymooners co-star Meadows long before they did the television series, working together in a summer stock production of No, No, Nanette. Randolph also portrayed Trixie Norton in skits on The Jackie Gleason Show. In a September 2015 interview, Randolph said that she did not portray Trixie Norton in Honeymooners revivals due to personal and geographic reasons; in addition, Randolph stated that Gleason considered her to be "the quintessential Trixie."
Other career
On Broadway, Randolph appeared in Ladies Night in a Turkish Bath. After she became identified with the Norton character, she seldom found other parts. "For years after that role," Randolph said, "directors would say: 'No, we can't use her. She's too well known as Trixie." She performed in summer stock musicals, made commercials, and had a few guest appearances on TV shows.
Personal life
Randolph married Richard Lincoln Charles, a wealthy marketing executive, on October 2, 1955, the day afterThe Honeymooners premiered. Richard Charles died in 1997 at age 74. Their son, Randolph Richard Charles, is a marketing executive. She is the grand aunt of former Major League Baseball pitcher Tim Redding.