SOLUTION: A pollster reports that 58% of American favor a law that is pending in Congress. The error is less than 2%. a. Write an absolute value inequality that describes the true percentag

Algebra.Com
Question 1199963: A pollster reports that 58% of American favor a law that is pending in Congress. The error is less than 2%.
a. Write an absolute value inequality that describes the true percentage p of
American who are in favor of the legislation.
b. Solve your inequality in part a for p.
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
**a) Write the absolute value inequality**
* Let 'p' represent the true percentage of Americans who favor the legislation.
* The error is less than 2%, meaning the difference between the reported percentage (58%) and the true percentage (p) is less than or equal to 2%.
* This can be expressed as:
|p - 58| ≤ 2
**b) Solve the inequality for p**
* **Case 1: p - 58 ≥ 0**
* p - 58 ≤ 2
* p ≤ 60
* **Case 2: p - 58 < 0**
* -(p - 58) ≤ 2
* -p + 58 ≤ 2
* -p ≤ -56
* p ≥ 56
* **Combine the solutions:**
* 56 ≤ p ≤ 60
**Therefore, the true percentage (p) of Americans who favor the legislation lies within the interval [56%, 60%].**
RELATED QUESTIONS

It is reported that in the Congress, 60% are in favor of the Death Penalty Law. If a... (answered by Edwin McCravy)
A bank’s head office is concerned about the accuracy of the reports being submitted by... (answered by stanbon)
The American Automobile Association (AAA) reports that of the fatal car and truck... (answered by roseo)
I NEED HELP IN STATISTICS. PLEASE HELP. THANK YOU SO MUCH. Quality Polls contends... (answered by stanbon)
A bank’s head office is concerned about the accuracy of the reports being submitted by... (answered by stanbon)
An auditor for American Health Insurance reports that 20% of policyholders submit a claim (answered by mathmate)
Vermont State legislators would like to think that a majority of voters favor their... (answered by ewatrrr)
A bill is sent to the President of the United States when it has passed both houses of... (answered by stanbon)
A study reports that the mean birth weight of 81 full-term infants is 6.1 pounds. The... (answered by Fombitz)