Final answer:
Benny Goodman was a clarinetist who led the best known jazz big band during the 1930s and 40s and was one of the most popular figures in the music industry.
Step-by-step explanation:
The clarinetist who led the best known jazz big band during the 1930s and 40s and was one of the most popular figures in the music industry was Benny Goodman.
Goodman's band, known as the Benny Goodman Orchestra or the King of Swing, achieved great success and popularity during that time. Goodman not only had a significant impact on jazz but also played a crucial role in bringing jazz to a wider audience beyond just jazz enthusiasts.