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.
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.
