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As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.

\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{6}{|c|}{ Eye Color } \\
\hline \begin{tabular}{c}
Hair \\
Color
\end{tabular} & Blue & Gray & Green & Brown & \begin{tabular}{c}
Marginal \\
Totals
\end{tabular} \\
\hline Blond & 42 & 5 & 21 & 10 & 78 \\
\hline Red & 12 & 22 & 19 & 12 & 65 \\
\hline Brown & 22 & 5 & 12 & 34 & 73 \\
\hline Black & 9 & 3 & 11 & 64 & 87 \\
\hline \begin{tabular}{c}
Marginal \\
Totals
\end{tabular} & 85 & 35 & 63 & 120 & 303 \\
\hline
\end{tabular}

From the sample population of students with gray eyes, what is the relative frequency of students with red hair?

A. 0.07

B. 0.12

C. 0.34

D. 0.63



Answer :

GinnyAnswer
To determine the relative frequency of students with red hair among those with gray eyes, we first need to look at the table and gather the necessary data:

1. Identify the total number of students with gray eyes.
2. Identify the number of students with gray eyes who also have red hair.
3. Calculate the relative frequency by dividing the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the table:
- The total number of students with gray eyes is 35.
- The number of students with gray eyes and red hair is 22.

Next, we calculate the relative frequency:

[tex]\[ \text{Relative Frequency} = \frac{\text{Number of students with gray eyes and red hair}}{\text{Total number of students with gray eyes}} \][/tex]

Substitute the values:

[tex]\[ \text{Relative Frequency} = \frac{22}{35} \approx 0.6285714285714286 \][/tex]

Hence, we match this computed relative frequency to the closest provided options. The closest match is:

D. 0.63

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