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Charles Vacca, 39, was shot on Monday morning (local time), then airlifted to a medical centre in Las Vegas and pronounced dead shortly before 9 p.m., the sheriff's office said.
Vacca was working at the Bullets and Burgers outdoor range in White Hills, about 100km southeast of Las Vegas, when the accident occurred. The girl and her parents were at the range while on vacation, a sheriff's spokeswoman told the Los Angeles Times.
He was standing next to the girl, instructing her how to use the Uzi, when she pulled the gun's trigger and the recoil sent the weapon over her head, causing him to be shot, the sheriff's office said.
"This is a rarity for something like this to happen," the spokeswoman said.