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Suppose cluster sampling were being used to survey digital camera users, who amount to [tex]$77 \%$[/tex] of the population of the United States. Based on the table below, which city would be considered the best cluster?

\begin{tabular}{|c|c|}
\hline
City & \begin{tabular}{c}
Percentage of the population \\
who are digital camera users
\end{tabular} \\
\hline
Houston & [tex]$96 \%$[/tex] \\
\hline
Las Vegas & [tex][tex]$11 \%$[/tex][/tex] \\
\hline
Phoenix & [tex]$49 \%$[/tex] \\
\hline
San Diego & [tex]$78 \%$[/tex] \\
\hline
\end{tabular}

A. Houston
B. San Diego
C. Phoenix
D. Las Vegas



Answer :

GinnyAnswer
To determine the best city cluster for surveying digital camera users, we need to find the city whose percentage of digital camera users is closest to the national percentage of 77%.

Let's compare the percentages for each city:

- Houston: 96%
- Las Vegas: 11%
- Phoenix: 49%
- San Diego: 78%

Next, we calculate the absolute differences between each city's percentage and the national percentage (77%):

- Houston: [tex]\(|96 - 77| = 19\)[/tex]%
- Las Vegas: [tex]\(|11 - 77| = 66\)[/tex]%
- Phoenix: [tex]\(|49 - 77| = 28\)[/tex]%
- San Diego: [tex]\(|78 - 77| = 1\)[/tex]%

The city with the smallest absolute difference is San Diego, with a difference of only 1%. Therefore, San Diego is the city whose percentage of digital camera users is closest to the national percentage of 77%.

Based on the given choices:
A. Houston
B. San Diego
C. Phoenix
D. Las Vegas

The best city cluster is:

B. San Diego

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