In 1976 who was the first woman to win an Olympic medal in shooting?

In 1976 the shooting competition was still mixed - different tournaments for men and women came only in 1984.

The American Margaret Murdock entered the competition for rifle three positions at 50 m. She tied with her compatriot Lanny Bassham, with a score of 1162 on 1200, while the bronze medal went to the German Werner Sebold with 1160.

Bassham's suggestion to hand out two gold medals was rejected, and close examination of the respective targets showed a slight advantage for Bassham. So Margaret Murdock won silver.

https://en.wikipedia.org/wiki/Shooting_at_the_1976_Summer_Olympics_%E2%80%93_Mixed_50_metre_rifle_three_positions