Car is cutting off

While waiting for the light to change my car cuts off. I had the batter checked and the machine said "Good! 93%" I checked to see if the alternator was working and took one of the cables off while car was running and it still ran fine. Dar Car said I needed and air filter would that make the car cut off like that? While washing the car I played the radio and the next time I went to start I had to get a jump. But that is what made me go and get the battery checked.
Please advise because the same thing happened to my coworker and she had an accident and totaled her truck because the car just cut off on her while turning and she was hit bad. Sincerely, Cynthia