Demographics and Population Statistics
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. 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.