On December 16, 2019 at about 13:23 CST, Envoy flight 3960, an EMB140, N805AE, encountered severe turbulence during cruise flight while enroute to Gainesville Regional Airport (KGNV), Gainesville, Florida. Of the 39 passengers and crew onboard, one passenger sustained serious injuries. The airplane was not damaged. The flight was operating under 14 Code of Federal Regulations Part 121 as a regularly scheduled domestic passenger flight from Dallas-Ft Worth International Airport (KDFW), Dallas, Texas, to KGNV. According to the flight crew, as the flight was cruising at flight level (FL) 370 in visual meteorological conditions, they could see convective activity ahead. Air traffic control informed them that pilot reports along their route of flight had reported "nothing worse than moderate chop" with one report of "severe turbulence" from a CRJ that was an hour old. About 50 miles from GNV, the captain made an announcement to the passengers about impeding weather and possible turbulence and requested that the flight attendant (FA) take her seat. The seat belt sign was illuminated. As the flight approached the weather, the first officer (FO), who was the pilot flying, began to maneuver around several cells visually. The airplane radar did not show any returns. Upon entering visible moisture, moderate rain and turbulence began immediately but increased rapidly in intensity. Airspeed and altitude began fluctuating rapidly and upon receiving an over speed warning, the FO retarded the thrust levers to idle and deployed the speed brakes. Large fluctuations in vertical speed continued to occur and the autopilot automatically disengaged simultaneously with stick shaker activation. EICAS displayed AUTOPILOT FAIL and YAW DAMPER FAIL. Shortly after, the FO returned the airplane to a normal flight condition and returned to FL 370. The captain informed ATC that the flight had encountered severe turbulence and then contacted the FA to check on if there were any injuries. At that time, the FA reported no injuries; however, approximately 5 minutes later the captain was informed that a passenger had been injured. According to the FA and deadheading crewmembers, all passengers and the FA were seated with their seatbelts fastened when the turbulence was encountered. After the turbulence stopped, drinks covered the walls and ceiling, and magazines and electronic devices were located multiple rows from their original location. The injured passenger indicated that her seatbelt, with extender, was fastened, however, she had hit her head “pretty hard” and had back and neck pain. The captain notified dispatch and ATC of the injury and requested that paramedics meet the airplane at the gate. After landing the injured passenger was transported to a local hospital and diagnosed with two small neck fractures. Post accident examination of the weather data determined that the flight encountered convectively induced turbulence after penetrating cumulonimbus clouds, with tops near FL400, while attempting to overfly a large area of known convection. In the area of the encounter, Weather Surveillance Radar depicted extreme echoes at lower altitudes with lighter echoes at the airplane’s altitude, with lightning in the vicinity. The National Weather Service (NWS) Convective Outlook had warned of a moderate risk of severe thunderstorms over the area. In addition, there was a NWS tornado watch and a Convective SIGMET current for severe embedded thunderstorms in the area.