Ms. Stewart teaches three science classes. Her students are freshmen and sophomores. Her student data are shown in the relative frequency table.

\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}

Which statement is false?

A. [tex]$30 \%$[/tex] of her students are in physical science.
B. [tex]$45 \%$[/tex] of her students are freshmen.
C. [tex]$25 \%$[/tex] of her students are in chemistry.
D. [tex]$35 \%$[/tex] of her students are in biology.



Answer :

Let's analyze the given data from the relative frequency table and verify each statement to determine which one is false.

The table is as follows:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline & \text{Biology} & \text{Chemistry} & \text{Physical Science} & \text{Total} \\ \hline \text{Freshmen} & 0.15 & 0.1 & 0.2 & 0.45 \\ \hline \text{Sophomores} & 0.2 & 0.25 & 0.1 & 0.55 \\ \hline \text{Total} & 0.35 & 0.35 & 0.3 & 1.0 \\ \hline \end{array} \][/tex]

Now, let's examine each statement:

Statement A: 30% of her students are in physical science.
- According to the total row for Physical Science, the value is 0.3, which means 30% of the students are in physical science.
- Therefore, Statement A is true.

Statement B: 45% of her students are freshmen.
- According to the total column for Freshmen, the value is 0.45, which means 45% of the students are freshmen.
- Therefore, Statement B is true.

Statement C: 25% of her students are in chemistry.
- According to the total row for Chemistry, the value is 0.35, which means 35% of the students are in chemistry.
- This does not match the 25% stated.
- Therefore, Statement C is false.

Statement D: 35% of her students are in biology.
- According to the total row for Biology, the value is 0.35, which means 35% of the students are in biology.
- Therefore, Statement D is true.

Therefore, the false statement is:
C. 25% of her students are in chemistry.