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

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



Answer :

GinnyAnswer
To determine which statement is false, we need to analyze each statement in conjunction with the data provided in the relative frequency table.

First, let's summarize the data presented in the table:

- Total students in Biology: 0.35
- Total students in Chemistry: 0.35
- Total students in Physical Science: 0.30
- Total freshmen: 0.45
- Total sophomores: 0.55

Now, let's evaluate each statement:

### Statement A: "35% of her students are in chemistry."
- From the table, the relative frequency for Chemistry is 0.35.
- Converting 0.35 to percentage: [tex]\(0.35 \times 100 = 35\%\)[/tex].
- This statement is true.

### Statement B: "20% of her students are in physical science."
- From the table, the relative frequency for Physical Science is 0.30.
- Converting 0.30 to percentage: [tex]\(0.30 \times 100 = 30\%\)[/tex].
- The statement claims that 20% of students are in Physical Science, but we see it is actually 30%.
- This statement is false.

### Statement C: "35% of her students are in biology."
- From the table, the relative frequency for Biology is 0.35.
- Converting 0.35 to percentage: [tex]\(0.35 \times 100 = 35\%\)[/tex].
- This statement is true.

### Statement D: "55% of her students are sophomores."
- From the table, the relative frequency for Sophomores is 0.55.
- Converting 0.55 to percentage: [tex]\(0.55 \times 100 = 55\%\)[/tex].
- This statement is true.

After evaluating each statement, the false statement is:

### Statement B: "20% of her students are in physical science"

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