Chapter 18, Problem 35E

(a)

To determine

To explain why the plot has this funnel shape.

Explanation of Solution

It is given in the question that a reporter working on a story of the New York lottery contacted one of the authors wanting to help analyzing the data to see if some tickets sales outlets were more likely to produce winners. The data of the outlets are graphed given in the question. And the reporter thinks that by identifying the outlets with the highest fraction of bets paid out players might be able to increase their chance of winning. Thus, by looking at the graph the plot has a funnel shape this is because smaller outlets have more variability than larger outlets as predicted by the Central Limit Theorem.

(b)

To determine

To explain why the reporter’s idea would not have worked anyway.

Explanation of Solution

It is given in the question that a reporter working on a story of the New York lottery contacted one of the authors wanting to help analysing the data to see if some tickets sales outlets were more likely to produce winners. The data of the outlets are graphed given in the question. And the reporter thinks that by identifying the outlets with the highest fraction of bets paid out players might be able to increase their chance of winning. Thus, the reporter’s idea would not have worked anyway because since the lottery is completely random, all outlets are equally likely to sell the winning ticket.