The National Transportation Safety Board said in a preliminary report Thursday that the pilot had purchased the Piper PA-24-250 airplane about a week earlier.
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The plane crashed Sunday afternoon at Coulter Airfield in Bryan, about 85 miles northwest of Houston. The NTSB said it came to rest on a grass field on the end of a runway.
Bryan police have identified those killed as 21-year-old Victoria Walker and her parents, 54-year-old David Walker and 51-year-old Tamara Walker.
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KBTX-TV identified the lone survivor of the crash as Luke Armstrong. He is still recovering in the hospital from his critical injuries. Armstrong is a senior at Texas A&M studying construction science, according to friends.
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The NTSB did not name the occupants of the plane but said in the report that the pilot, who was male, died. The four people aboard the plane had planned to do a sightseeing flight in the local area, according to the agency.
Police said the Walkers were from Farmersville, about 40 miles northeast of Dallas.
3 dead, 1 in critical condition after plane crash in Bryan
The Associated Press contributed to this report.