3. Different frogs were studied to determine what they prefer to eat. The results of this study are displayed in the two-way frequency table below:

\begin{tabular}{|c|c|c|c|}
\hline & Bullfrogs & Tree Frogs & Wood Frogs \\
\hline Dragonflies & 24 & 12 & 15 \\
\hline Worms & 19 & 20 & 30 \\
\hline
\end{tabular}

What is the marginal relative frequency for wood frogs that were studied?

A. [tex]$25.0 \%$[/tex]

B. [tex]$12.5 \%$[/tex]

C. [tex]$43.5 \%$[/tex]

D. [tex]$37.5 \%$[/tex]



Answer :

To determine the marginal relative frequency for wood frogs that were studied, we need to follow these steps:

1. Aggregate the Total Number of Frogs Studied:

Based on the table provided:

- For Dragonflies: 24 (Bullfrogs) + 12 (Tree Frogs) + 15 (Wood Frogs)
- For Worms: 19 (Bullfrogs) + 20 (Tree Frogs) + 30 (Wood Frogs)

Summing these up:
[tex]\[ 24 + 12 + 15 + 19 + 20 + 30 = 120 \][/tex]
So, the total number of frogs studied is 120.

2. Calculate the Total Number of Wood Frogs Studied:

From the table:
- 15 Wood Frogs prefer Dragonflies
- 30 Wood Frogs prefer Worms

Summing these up:
[tex]\[ 15 + 30 = 45 \][/tex]
So, the total number of Wood Frogs studied is 45.

3. Calculate the Marginal Relative Frequency:

The marginal relative frequency is the ratio of the number of Wood Frogs studied to the total number of frogs studied, expressed as a percentage. This can be calculated as follows:
[tex]\[ \frac{\text{Number of Wood Frogs}}{\text{Total Number of Frogs}} \times 100 = \frac{45}{120} \times 100 \][/tex]

4. Perform the Division and Multiplication:
[tex]\[ \frac{45}{120} \approx 0.375 \implies 0.375 \times 100 = 37.5\% \][/tex]

So, the marginal relative frequency for wood frogs that were studied is [tex]\(37.5\%\)[/tex].

Thus, the correct answer is:
[tex]\[ 37.5\% \][/tex]