Question

a research company surveys people in a community about a new recycling program. the company expects 6,000 people to respond favorably to the survey. if there is a percent error of 2.5%, what is the range of the number of people who are expected to respond favorably to the survey? enter the correct answers in the boxes. least number of people: greatest number of people:

Explanation:

Step1: Calculate the error amount

The percent error is \(2.5\%\), and the expected number of people is \(n = 6000\). The error amount \(e\) is calculated as \(e=6000\times2.5\%=6000\times\frac{2.5}{100}=150\).

Step2: Find the greatest number of people

The greatest number of people \(G\) is \(G = 6000+150\).

$$G=6150$$

Step3: Find the least number of people

The least number of people \(L\) is \(L=6000 - 150\).

$$L = 5850$$

Answer:

Greatest number of people: \(6150\)
Least number of people: \(5850\)