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A hardware store owner is replenishing his stock of base paint for an upcoming home improvement sale. He conducted a survey to determine which paint finish customers prefer on living room walls. The owner asked both homeowners and professional building contractors. The results of the survey are shown in the two-way relative frequency table.

\begin{tabular}{|r|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & Matte & Satin & Glossy & Total \\
\hline Homeowners & 4 & 10 & 12 & 26 \\
\hline Contractors & 2 & 13 & 9 & 24 \\
\hline Total & 6 & 23 & 21 & 50 \\
\hline
\end{tabular}

Approximately what percentage of contractors prefer the glossy finish?

A. [tex]$34.6\%$[/tex]
B. [tex]$42.9\%$[/tex]
C. [tex]$46.1\%$[/tex]
D. [tex]$37.5\%$[/tex]

Sagot :

GinnyAnsweridn
To determine the percentage of contractors who prefer the glossy finish, we need to follow these steps:

1. Identify the total number of contractors surveyed.
2. Identify the number of contractors who prefer the glossy finish.
3. Calculate the percentage of contractors who prefer the glossy finish by dividing the number of glossy-preferring contractors by the total number of contractors, and then multiplying by 100.

From the table:
- The total number of contractors surveyed is 24.
- The number of contractors who prefer the glossy finish is 9.

Now, let's calculate the percentage:

[tex]\[ \text{Percentage of contractors who prefer the glossy finish} = \left( \frac{\text{Number of contractors preferring glossy}}{\text{Total number of contractors}} \right) \times 100 \][/tex]

Substituting the numbers:

[tex]\[ \text{Percentage of contractors who prefer the glossy finish} = \left( \frac{9}{24} \right) \times 100 = 37.5\% \][/tex]

Therefore, the correct answer is:

D. [tex]$37.5 \%$[/tex]
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