Examples are predicting how the supreme court justices will vote based on their past records. In this example, the statistical model is better at predicting outcomes than a panel of very experienced court watchers. Another example from the medical field is tools that can assist doctors make better patient evaluations and diagnosis. Companies can use models and how an applicant answers a quiz to predict how long they will work are most interesting.
Lots of interesting ideas here.
This book is also an interesting read when done side-by-side with 'The Black Swan' which will be another post.