JSM 2005 - Toronto

Abstract #303518

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 456
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics in Sports
Abstract - #303518
Title: On Successive Proportions of Binary Sequences
Author(s): Laurence D. Robinson*+ and Mihai Caragiu
Companies: Ohio Northern University and Ohio Northern University
Address: Department of Mathematics, Ada, OH, 45810, United States
Keywords: Binary sequences ; successive proportions ; intermediate value theorem ; free throws
Abstract:

In the 65th Annual William Putnam Mathematical Competition, the following question is posed: "Basketball star Shanille O'Keal's team statistician keeps track of the number, S(N), of successful free throws she has made in her first N attempts of the season. Early in the season, S(N) was less than 80% of N, but by the end of the season, S(N) was more than 80% of N. Was there necessarily a moment in between when S(N) was exactly 80% of N?" In this paper, we answer this question and obtain a more general result using an intermediate value theorem for binary sequences.


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