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Difference between revisions of "2006 AMC 8 Problems/Problem 8"

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The graph shows the birth month of 100 famous Americans. What percent of these people have March as their birth month?
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== Problem ==
  
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The data in the stem and leaf plot shown are the long jump distances, in centimeters, that the girls team of Pseudo H.S. made at practice today. <math>(51|1</math> represents <math>511</math> centimeters<math>.)</math> What is the sum of the median and mode of the data?
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The table shows some of the results of a survey by radiostation KAMC. What percentage of the males surveyed listen to the station?
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<math> \begin{tabular}{|c|c|c|c|}\hline & Listen & Don't Listen & Total\\ \hline Males & ? & 26 & ?\\ \hline Females & 58 & ? & 96\\ \hline Total & 136 & 64 & 200\\ \hline\end{tabular} </math>
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<math> \textbf{(A)}\ 39\qquad\textbf{(B)}\ 48\qquad\textbf{(C)}\ 52\qquad\textbf{(D)}\ 55\qquad\textbf{(E)}\ 75 </math>
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== Solution ==
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Filling out the chart, it becomes
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<math> \begin{tabular}{|c|c|c|c|}\hline & Listen & Don't Listen & Total\\ \hline Males & 78 & 26 & 104\\ \hline Females & 58 & 38 & 96\\ \hline Total & 136 & 64 & 200\\ \hline\end{tabular} </math>
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Thus, the percentage of males surveyed that listen to the station is <math> 100 \cdot \frac{78}{104} \%= \boxed{\textbf{(E)}\ 75 \%} </math>.
  
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\begin{tabular}{l|lllll}
 
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51& 1\\
 
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52&\\
 
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53& 2& 5\\
 
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54& 0& 2& 2& 5\\
 
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55& 0& 1& 3& 4& 7\\
 
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56& 0& 2& 5\\
 
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57& 0& 1\\
 
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\end{tabular}
 
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2006|num-b=7|num-a=9}}
 
{{AMC8 box|year=2006|num-b=7|num-a=9}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 17:05, 3 January 2023

Problem

The table shows some of the results of a survey by radiostation KAMC. What percentage of the males surveyed listen to the station?

$\begin{tabular}{|c|c|c|c|}\hline & Listen & Don't Listen & Total\\ \hline Males & ? & 26 & ?\\ \hline Females & 58 & ? & 96\\ \hline Total & 136 & 64 & 200\\ \hline\end{tabular}$

$\textbf{(A)}\ 39\qquad\textbf{(B)}\ 48\qquad\textbf{(C)}\ 52\qquad\textbf{(D)}\ 55\qquad\textbf{(E)}\ 75$

Solution

Filling out the chart, it becomes

$\begin{tabular}{|c|c|c|c|}\hline & Listen & Don't Listen & Total\\ \hline Males & 78 & 26 & 104\\ \hline Females & 58 & 38 & 96\\ \hline Total & 136 & 64 & 200\\ \hline\end{tabular}$

Thus, the percentage of males surveyed that listen to the station is $100 \cdot \frac{78}{104} \%= \boxed{\textbf{(E)}\ 75 \%}$.


See Also

2006 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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