Answer: [tex]|x-12.8|\leq3.93[/tex]
The interval in which the average is likely to fall : [tex]8.87\leq x\leq16.73[/tex]
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 :-
[tex]|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[/tex]
Hence, the interval in which the average is likely to fall : [tex]8.87\leq x\leq16.73[/tex]
