Police said the incident happened around 5:30 p.m. when a female passenger became angry and threw a soda bottle through a windshield, according to witnesses.
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Witnesses said she started to argue with the bus driver and a male passenger attempted to intervene.
The female slashed the male passenger's neck with a box cutter, according to the witnesses, and then got off the bus.
According to police, the male passenger was taken to the hospital for treatment for injuries that did not appear to be life-threatening.
The suspect is described as a black female in her 20s, about 5'4, with a medium build and a medium to light complexion with red hair.
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She was wearing a dark top with stripes on the sleeves and brown animal print leggings, according to police.
Police said she was carrying a small child.
Anyone with information is asked to call Investigator Junker at (919) 560-4935, ext. 29416 or CrimeStoppers at (919) 683-1200.