On August 8, 2019, about 1547 central daylight time, a Bombardier CL-600-2B16 business jet, N237QS, was involved in an accident while flying at flight level (FL)335 in the vicinity of Lubbock, Texas. The pilot and co-pilot were not injured. The flight attendant sustained minor injuries, 1 passenger sustained serious injuries, 1 passenger sustained minor injuries, and 5 passengers were not injured. The business flight was being operated under the provisions of Title 14 Code of Federal Regulations Part 91. The aircraft was climbing through flight level (FL) 335 to the assigned altitude of FL340. The airplane was in an approximate 500-foot per minute rate of climb when unexpected wake turbulence was encountered. The captain, who was at the controls, reported that prior to the event, the aircraft was in smooth air when suddenly, the airplane started to shudder and quickly rolled left and back to the right. The airplane pitched up and down as it rolled. The autopilot (AP) was on, so the captain disconnected the AP and tried to stabilize. The passenger seat belt sign was off. The flight attendant reported that unsecured objects in the cabin were thrown about, including passengers and the flight attendant. Cabin service items (food, broken plates, and dishware), and the lavatory fluid spilled on the interior of the cabin. After the event, the flight crew stabilized and assessed the aircraft, believing it was wake turbulence, they advised ATC of the event, and requested a climb to FL360 to be above any other potential wake. According to the flight crew, an immediate assessment of injuries was completed by the flight attendant, and the captain went to the cabin to check on the passengers and flight attendant. After accessing the injuries, the captain made an immediate decision to divert the flight. The flight crew coordinated a destination change to Lubbock, Texas, with ATC and advised the company. A normal approach and landing were made at Lubbock, Texas (LBB). Emergency services met the aircraft upon arrival and assessed the crew and passengers. Two passengers were transported to the hospital. One passenger was treated and released with minor injuries and the other was admitted with a tibia fracture which required surgery. The flight attendant was standing in the galley at the time of the event and reported several minor injuries. She was escorted to the hospital by the flight crew and was treated and released. A review of flight data showed at the time of the event the aircraft was between eight and ten miles in trail of FedEx Flight 3154, an Airbus A300 enroute from Fort Worth Alliance (AFW) to Burbank Bob Hope Airport (BUR). The FedEx Flight was level at FL340 and on the same assigned route as N237QS. During the event, FDR data reported winds from 336° (right quartering headwind) at 77 knots for one data plot. The flight crew was not aware of the preceding FedEx Airbus until after the wake turbulence encounter. According to Flight Data Recorder (FDR) data, the wake turbulence lasted 11 seconds during which a maximum bank of 23.4° right and 12.6° left were encountered. The pitch reached a maximum of 8.5° nose up and -2.5° nose down during this time, while the airspeed was stable between 268 and 276 knots. Heading started at 280 degrees and initially went left to 272° before oscillating to 282° (after 2 seconds) and back to 269° (2 seconds later).