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The two-way table represents data from a survey asking students whether they plan to attend college, travel, or both after high school.

Plans after High School
\begin{tabular}{|c|c|c|c|}
\hline & College & Not College & Total \\
\hline Travel & 43 & 10 & 53 \\
\hline Not Travel & 24 & 5 & 29 \\
\hline Total & 67 & 15 & 82 \\
\hline
\end{tabular}

Which is the marginal relative frequency for students who plan to attend college? Round the answer to the nearest percent.

A. 18%
B. 22%

Sagot :

To calculate the marginal relative frequency for students who plan to attend college, follow these detailed steps:

1. Identify the total number of students:
From the table, we see that the total number of students surveyed is listed in the bottom-right corner, which is [tex]\(82\)[/tex].

2. Identify the number of students who plan to attend college:
The total number of students planning to attend college is given in the cell corresponding to the "College" column in the "Total" row, which is [tex]\(67\)[/tex].

3. Calculate the marginal relative frequency:
The marginal relative frequency is calculated by dividing the number of students who plan to attend college by the total number of students. Then, we convert this fraction into a percentage by multiplying by [tex]\(100\%\)[/tex].

So, we calculate:
[tex]\[ \text{Marginal Relative Frequency} = \left(\frac{67}{82}\right) \times 100\% \][/tex]

4. Resulting Calculation:
The resulting calculation for the marginal relative frequency is approximately [tex]\(81.70731707317073\%\)[/tex].

5. Rounding the result to the nearest percent:
When we round [tex]\(81.70731707317073\%\)[/tex] to the nearest whole number, we get [tex]\(82\%\)[/tex].

Therefore, the marginal relative frequency for students who plan to attend college, rounded to the nearest percent, is [tex]\(82\%\)[/tex].