1.00 +: 0.75 0.50 0.25 0.00 200,000 400,000 600,000 800,000 TotalSales TotalPaid/TotalSales
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.)
a) Explain why the plot has this funnel shape.
b) Explain why the reporter’s idea wouldn’t have worked
anyway.
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