The Sundance Film Festival is held every January in Park City, Utah. Individuals from the film community determine various awards for independent film makers, and audience awards are also presented. In 2012, approximately 17% of the feature films in the documentary category were directed by women. Suppose a sample of 30 documentary films are selected at random

 

 

(a) What is the probability (0.0001) that exactly six films were directed by women?

 

 

(b) What is the probability (0.0001) that at least nine films were directed by women? 

 

(c) Suppose three films were directed by women. Is there any evidence to suggest that the proportion of films directed by women is different from 0.17?