The daughter of a Carson City fire captain made the cut Wednesday night on "American Idol" putting her among 24 contestants to begin performing live on the Fox broadcast next week.Amanda Avila, 23, was one of the last two female singers standing when she beat out Jaclyn Crum, 16, in the final 10 minutes of the program.In all, 100,000 people tried out for a coveted spot in the top 24 on American's No. 1 television program.Avila, a siren for the Treasure Island Hotel and Casino in Las Vegas, attended the Los Angeles School of Performing Arts and sang backup for …