The Social Security death index shows Annie E. Groat was born 16 Mar 1920. She was a resident of NC when she got her S.S.# Her residence at the time of her death was Frostproof, FL; she died 21 Dec 1989.
Recommend you ask family about her parents and siblings. If that is not proctical then try to find obituary and obtain death certificate. You may also obtain her Social security number application.