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The residents of three towns were polled to find the percentage of residents who take a vacation in the summer or in the winter.

\begin{tabular}{|c|c|c|c|}
\hline & Summer & Winter & Total \\
\hline Town 1 & 567 & 87 & 654 \\
\hline Town 2 & 345 & 102 & 447 \\
\hline Town 3 & 143 & 158 & 301 \\
\hline Total & 1,055 & 347 & 1,402 \\
\hline
\end{tabular}

Which is the joint relative frequency of those in Town 2 who take a summer vacation? Round the answer to the nearest percent.

A. [tex]$70 \%$[/tex]



Answer :

GinnyAnswer
To find the joint relative frequency of residents in Town 2 who take a summer vacation, follow these steps:

1. Identify the relevant data: From the table, note the number of Town 2 residents who take a summer vacation and the total number of residents in Town 2.
- Town 2 residents who take a summer vacation: 345
- Total residents in Town 2: 447

2. Calculate the joint relative frequency: Use the formula for joint relative frequency, which is the ratio of the subgroup to the overall group, multiplied by 100 to convert it to a percentage.
[tex]\[ \text{Joint Relative Frequency} = \left( \frac{\text{Number of summer vacationers in Town 2}}{\text{Total number of residents in Town 2}} \right) \times 100 \][/tex]
Substituting in the numbers:
[tex]\[ \text{Joint Relative Frequency} = \left( \frac{345}{447} \right) \times 100 \][/tex]

3. Interpret the result: The result of this division is 77.18120805369128%.

4. Round to the nearest percent: To give a rounded percentage, we round 77.18120805369128 to the nearest whole number, which is 77%.

Thus, the joint relative frequency of those in Town 2 who take a summer vacation, rounded to the nearest percent, is 77%.

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