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.22 Suppose a sample of 35 documentary films are selected at random.
a. What is the probability that exactly five films were directed by women?
b. What is the probability that at least eight 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? Justify your answer.
In Illinois, a typical DUI (Driving Under the Influence) offender is a 34-year-old male, arrested between 11 p.m. and 4 a.m. on a weekend, and has a BAC (blood alcohol content) of 0.16. Eighty-five percent of all drivers arrested in Illinois are first-time offenders.23 Suppose 40 people arrested for DUI in Illinois are selected at random.
a. What is the probability that at least 12 are first-time offenders?
b. What is the probability that between 7 and 10 (inclusive) are first-time offenders?
c. Suppose 4 of those arrested are first-time offenders. Is there any evidence to suggest that the proportion of first-time offenders arrested for DUI in Illinois has changed? Justify your answer.