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 Freshmen & 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]$20 \%$[/tex] of her students are in physical science.
B. [tex]$55 \%$[/tex] of her students are sophomores.
C. [tex]$35 \%$[/tex] of her students are in biology.
D. [tex]$35 \%$[/tex] of her students are in chemistry.



Answer :

To determine which statement is false based on the given data, let's analyze the table carefully:

[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]

Let's go through each statement one by one and check their validity based on the table:

Statement A: [tex]$20 \%$[/tex] of her students are in physical science.
- The total percentage of students in physical science is provided in the table as [tex]\(0.3\)[/tex] or [tex]\(30\%\)[/tex].
- Comparing this with [tex]\(20\%\)[/tex], we see that [tex]\(20\%\)[/tex] is not equal to [tex]\(30\%\)[/tex].

Statement A is false.

Statement B: [tex]$55 \%$[/tex] of her students are sophomores.
- According to the table, the total percentage of sophomores is [tex]\(0.55\)[/tex] or [tex]\(55\%\)[/tex].
- This matches the statement exactly.

Statement B is true.

Statement C: [tex]$35 \%$[/tex] of her students are in biology.
- The total percentage of students in biology is given as [tex]\(0.35\)[/tex] or [tex]\(35\%\)[/tex].
- This matches the statement exactly.

Statement C is true.

Statement D: [tex]$35 \%$[/tex] of her students are in chemistry.
- The total percentage of students in chemistry is provided as [tex]\(0.35\)[/tex] or [tex]\(35\%\)[/tex].
- This matches the statement exactly.

Statement D is true.

After analyzing all the statements, the false one is:

Statement A: [tex]$20 \%$[/tex] of her students are in physical science.

The correct percentage is [tex]\(30 \%\)[/tex], not [tex]\(20 \%\)[/tex]. Thus, the false statement is statement [tex]\(A\)[/tex].