Well, to make a long story short, Benny Goodman was Jewish!
Since Benny Goodman's mother was Jewish, and in Orthodox Judaism and Conservative Judaism, those with a Jewish mother (or those who underwent a halakhic conversion) are considered Jewish, then that makes him Jewish. His father was Jewish too.
Benny Goodman (whose full birth name was Benjamin David Goodman) was born on May 30, 1909 in Chicago, Illinois. Benny Goodman passed away on June 13, 1986 (aged 77).
He was an American jazz and swing musician, clarinetist and bandleader, known as the ''King of Swing''.
If you see any details that require update, please Let us know!