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A relative frequency table is made from data in a frequency table.

Frequency Table
\begin{tabular}{|c|c|c|c|}
\hline & C & D & Total \\
\hline A & 15 & 25 & 40 \\
\hline B & 24 & 12 & 36 \\
\hline Total & 39 & 37 & 76 \\
\hline
\end{tabular}

Relative Frequency Table
\begin{tabular}{|l|l|l|l|}
\hline & C & D & Total \\
\hline A & 20\% & 33\% & 53\% \\
\hline B & 32\% & 16\% & 48\% \\
\hline Total & 52\% & 49\% & 100\% \\
\hline
\end{tabular}

What is the value of [tex]$g$[/tex] in the relative frequency table?
Round the answer to the nearest percent.

A. [tex]$25 \%$[/tex]
B. [tex]$33 \%$[/tex]
C. [tex]$63 \%$[/tex]
D. [tex]$68 \%$[/tex]



Answer :

GinnyAnswer
To determine the value of \( g \) in the relative frequency table, let's focus on finding the relative frequency of D given A.

The original frequency table shows:

| | C | D | Total |
|---|----|----|-------|
| A | 15 | 25 | 40 |
| B | 24 | 12 | 36 |
| Total | 39 | 37 | 76 |

First, we need to find the total frequency for D across all categories:

[tex]\[ \text{Total D} = 37 \][/tex]

Next, we identify the frequency of D given A, which is 25.

To calculate the relative frequency of D given A, we use the following formula:

[tex]\[ \text{Relative Frequency of D given A} = \left(\frac{\text{Frequency of D given A}}{\text{Total Frequency of D}}\right) \times 100 \][/tex]

Plugging in the values:

[tex]\[ \text{Relative Frequency of D given A} = \left(\frac{25}{76}\right) \times 100 \][/tex]

This calculation gives:

[tex]\[ \left(\frac{25}{76}\right) \times 100 = 32.89473684210527 \][/tex]

When rounded to the nearest percent, this value becomes:

[tex]\[ 33\% \][/tex]

Therefore, the value of \( g \) in the relative frequency table is:

[tex]\[ g = 33\% \][/tex]

Hence, the correct answer is:

[tex]\[ 33\% \][/tex]

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