students in 10th and 11th grade were asked whether they have a job. the raw data was converted to relative frequencies and recorded in the table below. given the conditional relative frequency table by column, what does the 0.14 represent? \
$\begin{tabular}{|c|c|c|c|} \\hline & 10th grade & 11th grade & total \\\\ \\hline job & 0.14 & 0.25 & 0.20 \\\\ \\hline no job & 0.86 & 0.75 & 0.80 \\\\ \\hline total & 1 & 1 & 1 \\\\ \\hline \\end{tabular}$
\bigcirc given that a student is a 10th grader, there is a 14\\% chance he or she has a job. \bigcirc given that a student has a job, there is a 14\\% chance he or she is a 10th grader. \bigcirc 14\\% of the students surveyed are 10th graders who have a job. \bigcirc 14\\% of the students are 10th graders.

Question

students in 10th and 11th grade were asked whether they have a job. the raw data was converted to relative frequencies and recorded in the table below. given the conditional relative frequency table by column, what does the 0.14 represent? \

\begin{tabular}{|c|c|c|c|} \\hline & 10th grade & 11th grade & total \\\\ \\hline job & 0.14 & 0.25 & 0.20 \\\\ \\hline no job & 0.86 & 0.75 & 0.80 \\\\ \\hline total & 1 & 1 & 1 \\\\ \\hline \\end{tabular}

\bigcirc given that a student is a 10th grader, there is a 14\\% chance he or she has a job. \bigcirc given that a student has a job, there is a 14\\% chance he or she is a 10th grader. \bigcirc 14\\% of the students surveyed are 10th graders who have a job. \bigcirc 14\\% of the students are 10th graders.

Accepted Answer

# Brief Explanations:
A conditional relative frequency table by column means we look at the relative frequency within each column (10th grade and 11th grade). The value 0.14 is in the "Job" row and "10th Grade" column. So it represents the proportion of 10th - grade students who have a job, given that the student is in 10th grade. In other words, given that a student is a 10th grader, the chance (or relative frequency) that he or she has a job is 0.14 or 14%.

Let's analyze the other options:
- Option 2: For the "given that a student has a job" case, we would look at the "Job" row totals and the values in the "10th Grade" and "11th Grade" columns relative to the "Job" row total. The "Job" row total is 0.20, and 0.14/0.20 = 0.7, so this is incorrect.
- Option 3: 14% of all students surveyed who have a job would be related to the "Job" row total, but 0.14 is within the "10th Grade" column, not the overall total, so this is incorrect.
- Option 4: The total for 10th grade is 1 (or 100%), but 0.14 is not the proportion of 10th graders in the overall student population. The overall proportion of 10th graders would be calculated from the total row, but 0.14 is within the "Job" sub - category of 10th graders, so this is incorrect.

# Answer:
Given that a student is a 10th grader, there is a 14% chance he or she has a job.

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