To find the relative frequency of direct hits that were category 3 hurricanes, we need to understand how this frequency is calculated and interpret the data correctly.
Here's a step-by-step solution:
1. Identify the total number of hurricanes observed:
From the table, we sum the frequencies of all hurricane categories:
[tex]\[
\text{Total hurricanes observed} = 115 + 107 + 65 + 15 + 4 = 306
\][/tex]
2. Identify the number of category 3 hurricanes:
According to the table, there are 65 category 3 hurricanes.
3. Calculate the relative frequency:
The relative frequency is given by the ratio of the number of category 3 hurricanes to the total number of hurricanes observed. Mathematically, it is:
[tex]\[
\text{Relative frequency} = \frac{\text{Number of category 3 hurricanes}}{\text{Total number of hurricanes observed}}
= \frac{65}{306}
\][/tex]
4. Interpret the ratio:
We have previously calculated or been given this value as:
[tex]\[
\text{Relative frequency} \approx 0.2124
\][/tex]
Thus, the relative frequency of direct hits that were category 3 hurricanes is approximately 0.2124.
Therefore, the correct answer is [tex]\(\boxed{0.2124}\)[/tex].
