The Chamber of Commerce is creating a survey for their city of 6,500 people. They would like a survey response rate of at least 75 percent. At least how many people must be surveyed in order to make the results generalizable to the larger population?(1 point) Responses 4,875 people 4,875 people 10 people 10 people 65 people 65 people 650 people

1 answer

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.