To determine which statement is false, let's analyze the data provided in the relative frequency table:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & Biology & Chemistry & \begin{tabular}{c}
Physical \\
science
\end{tabular} & Total \\
\hline Freshman & 0.15 & 0.1 & 0.2 & 0.45 \\
\hline Sophomores & 0.2 & 0.25 & 0.1 & 0.55 \\
\hline Total & 0.35 & 0.35 & 0.3 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Now, let's examine each statement:
A. [tex]$35\%$[/tex] of her students are in chemistry.
We look at the total percentage under Chemistry, which is [tex]\(0.35\)[/tex] or [tex]\(35\%\)[/tex].
This statement is true.
B. [tex]$55\%$[/tex] of her students are sophomores.
We look at the total percentage under Sophomores, which is [tex]\(0.55\)[/tex] or [tex]\(55\%\)[/tex].
This statement is true.
C. [tex]$20\%$[/tex] of her students are in physical science.
We look at the total percentage under Physical Science, which is [tex]\(0.3\)[/tex] or [tex]\(30\%\)[/tex]. This does not match the [tex]\(20\%\)[/tex] mentioned in the statement.
This statement is false.
D. [tex]$35\%$[/tex] of her students are in biology.
We look at the total percentage under Biology, which is [tex]\(0.35\)[/tex] or [tex]\(35\%\)[/tex].
This statement is true.
The false statement among the given options is:
C. [tex]$20\%$[/tex] of her students are in physical science.
Therefore, the answer is [tex]\(3\)[/tex], which corresponds to statement C.
