Use the following information to answer the Questions
Consider the following distribution of 32 voters at eight different positions over the interval [0, 1]. $$\begin{array} { | l | l | l | l | l | l | l | l | l | }
\hline \text { Location } & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \
\hline \begin{array} { l }
\text { Number of } \
\text { voters }
\end{array} & 1 & 6 & 2 & 7 & 7 & 2 & 6 & 1 \
\hline
\end{array}$$
-Assume that Candidate A and Candidate B's policy positions are 0.3 and 0.8. If Candidate C enters at 0.55, what fraction of the vote does the winner receive?

Question

Use the following information to answer the Questions
Consider the following distribution of 32 voters at eight different positions over the interval [0, 1]. $$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline \text { Location } & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \
\hline \begin{array} { l } 
\text { Number of } \
\text { voters }
\end{array} & 1 & 6 & 2 & 7 & 7 & 2 & 6 & 1 \
\hline
\end{array}$$
-Assume that Candidate A and Candidate B's policy positions are 0.3 and 0.8. If Candidate C enters at 0.55, what fraction of the vote does the winner receive?

Quizplus · Accepted Answer

We first find the distances between the candidates and Candidate C:

Candidate A: 0.55 - 0.3 = 0.25 
Candidate B: 0.8 - 0.55 = 0.25

Thus, for Candidate C to win, they need to receive all the votes between 0.3 and 0.8, inclusive.

These votes are split between Candidates A and B as follows:

Candidate A: 6 + 2 = 8 
Candidate B: 7 + 2 + 6 = 15

Therefore, the total number of votes Candidate C needs to win is 32 - 8 - 15 = 9.

Thus, the fraction of the vote the winner receives is 9/32, which is answer choice B.

Use the Following Information to Answer the Questions Consider the Following

Use the Following Information to Answer the Questions
Consider the Following