Not all NBA coaches who enjoyed lengthy careers were consistently putting together winning seasons with the teams they coached. For example, Bill Fitch, who coached for 25 seasons of professional basketball after starting his coaching career at the University of Minnesota, won 944 games but lost 1106 while working with the Cavaliers, Celtics, Rockets, Nets, and Clippers. If you were to randomly select 60 box scores from the historical records of games in which Bill Fitch coached one of the teams, what is the probability that less than half of them show his team winning?

To obtain your answer, use the normal approximation to the binomial distribution.

Source: http://www.basketball-reference.com