Chapter 15, Problem 47E

Lucky spot? A reporter working on a story about the New York lottery contacted one of the authors of this book, wanting help analyzing data to see if some ticket sales outlets were more likely to produce winners. His data for each of the 966 New York lottery outlets are graphed below; the scatterplot shows the ratio TotalPaid/TotalSales vs. TotalSales for the state’s “instant winner” games for all of 2007.

The reporter thinks that by identifying the outlets with the highest fraction of bets paid out, players might be able to increase their chances of winning. Typically—but not always—instant winners are paid immediately (instantly) at the store at which they are purchased. However, the fact that tickets may be scratched off and then cashed in at any outlet may account for some outlets paying out more than they take in. The few with very low payouts may be on interstate highways where players may purchase cards but then leave.

1. a) Explain why the plot has this funnel shape.
2. b) Explain why the reporter’s idea wouldn’t have worked anyway.