To find the joint relative frequency of being a child who prefers grapes, follow these steps:
1. Determine the specific category of interest. Here, the category is children who prefer grapes, which corresponds to 85 children.
2. Identify the total number of respondents. This is given in the table as the total number across all categories, which is 445.
3. Calculate the joint relative frequency. The joint relative frequency is found by dividing the number of children who prefer grapes by the total number of respondents. This can be expressed as:
[tex]\[
\text{Joint Relative Frequency} = \frac{\text{Number of children who prefer grapes}}{\text{Total number of respondents}}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Joint Relative Frequency} = \frac{85}{445}
\][/tex]
4. Interpret the result. This calculation gives the proportion of the total respondents who are children and prefer grapes.
Based on the options provided:
- A is incorrect because it divides by 202, which is the total number of people who prefer grapes.
- C is incorrect because it divides by 217, which is only the total number of children.
- D is incorrect because it divides 202 by 217, mixing fruit preference totals incorrectly.
Thus, the correct option is:
B. Divide 85 by 445.
So, the correct joint relative frequency of being a child who prefers grapes is approximately [tex]\(0.19101123595505617\)[/tex], or about 19.1%.
