To determine the minimum number of people that need to be surveyed to achieve a 75% response rate from a population of 6,500, we can set up the problem as follows:
Let \( x \) be the number of people surveyed. To achieve at least a 75% response rate, the number of responses required is:
\[ 0.75 \times 6500 = 4875 \]
The response rate is given by:
\[ \text{Response Rate} = \frac{\text{Number of responses}}{\text{Number of people surveyed}} = \frac{0.75x}{x} \]
To ensure that the expected responses meet or exceed 4,875 at a 75% response rate, we can write:
\[ 0.75x \geq 4875 \]
Now, solving for \( x \):
\[ x \geq \frac{4875}{0.75} = 6500 \]
Thus, at least 6,500 people need to be surveyed to achieve a 75% response rate that yields at least 4,875 responses.
Thus, from the provided options, the only number that meets this requirement is:
4,875 people.