Question

A poll found that a particular group of people read an average of 12.8 books per year. The pollsters are​ 99% confident that the result from this poll is off by fewer than 3.93 books from the actual average x. Express this situation as an inequality involving absolute​ value, and solve the inequality for x to determine the interval in which the average is likely to fall.

Answer 1

Answer: $|x-12.8|\leq3.93$

The interval in which the average is likely to fall : $8.87\leq x\leq16.73$

Step-by-step explanation:

Given : A poll found that a particular group of people read an average of 12.8 books per year.

The pollsters are​ 99% confident that the result from this poll is off by fewer than 3.93 books from the actual average x.

The inequality to express this situation involving absolute​ value will be :-

$|x-12.8|\leq3.93\\\\\Rightarrow\ -3.93\leq x-12.8\leq3.93 \\\\\text{Add 12.8 on both sides , we get}\\\\\Rightarrow\ -3.93+12.8\leq x\leq3.93+12.8\\\\\text{Simplify}\\\\\Rightarrow\ 8.87\leq x\leq16.73$

Hence, the interval in which the average is likely to fall : $8.87\leq x\leq16.73$