norman was trained at howard university, the peabody institute, and the university of michigan. her career began in europe, where she won the ard international music competition in munich in 1968, which led to a contract with the deutsche oper berlin. her operatic début came as elisabeth in wagner's "tannhäuser", after which she sang as verdi's aida at la scala in milan. she made her debut united states operatic appearance in 1982 with the opera company of philadelphia, when cast as jocasta in stravinsky's "oedipus rex", and as dido in purcell's "dido and aeneas". she went on to sing leading roles with many other companies, including the metropolitan opera, the lyric opera of chicago, the paris opera, and the royal opera, london. she sang at the second inauguration of ronald reagan, at queen elizabeth ii's 60th birthday celebration in 1986, and performed the "la marseillaise" to celebrate the 200th anniversary of the french revolution on july 14, 1989. she sang at the 1996 summer olympics opening ceremony in atlanta and for the second inauguration of bill clinton in 1997.