Chapter 3.7, Problem 38P

In a sports poll, $53\%$ of those surveyed believe their high school football team will win the state championship. The poll shows a margin of error of ±5 percentage points. Write and solve an absolute value inequality to find the least and the greatest percent of people that think their team will win the state championship.

To determine

The least and greatest percent of people that think their team will win the state champion by solving an absolute value inequality.

Answer to Problem 38P

Greatest percent of people that think for high school to win is 58%.

Least percent of people that think for high school to win is 48%.

Explanation of Solution

Given:

Percentage of people believed that their high school team will win the state champion is $53$ %.

Poll show a margin of error $\pm 5$ percentage.

Let total number of people be $x$ .

The percentage of people believe for high school will win the state championship is $53\%$

The it is expressed as:

  $=x\times \frac{53}{100}=0.53x$

Now, the number of people fall in error margin is $\pm x\times \frac{5}{100}=\pm 0.05x$ .

So, greatest percent of people think for high school win is $\left(\frac{0.53x+0.05x}{x}\right)\times 100=58\%$ .

Similarly, least percent of people think for high school win is $\left(\frac{0.53x-0.05x}{x}\right)\times 100=48\%$ .