The counselor converts the frequency table to a conditional relative frequency table by column.

English Grade vs. Number of Languages Studied

[tex]\[
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
\multicolumn{1}{c|}{} & 90 or Above & Lower than 90 & Total \\
\hline
English Only & 0.12 & 0.28 & $X$ \\
\hline
\begin{tabular}{c}
English and \\
Another \\
Language
\end{tabular} & 0.88 & 0.72 & Y \\
\hline
Total & 1.0 & 1.0 & 1.0 \\
\hline
\end{tabular}
\][/tex]

What is the value of [tex]$X$[/tex]?

A. 0.16
B. 0.20
C. 0.24
D. 0.40



Answer :

To determine the value of [tex]\( X \)[/tex], we need to analyze the table and focus on the row "English Only".

The table gives us the following information under the "English Only" category:
- The proportion of students who scored 90 or above in English and studied only English: [tex]\( 0.12 \)[/tex]
- The proportion of students who scored lower than 90 in English and studied only English: [tex]\( 0.28 \)[/tex]

To find the total proportion of students who studied only English (regardless of their English grade), we need to add these two proportions together:

[tex]\[ X = 0.12 + 0.28 \][/tex]

When we perform the addition:

[tex]\[ X = 0.40 \][/tex]

Thus, the value of [tex]\( X \)[/tex] is [tex]\( \boxed{0.40} \)[/tex].