Answer with explanation:
Given : A poll found that a particular group of people read an average of 15.7 books per year.
i.e. [tex]\mu=15.7[/tex]
The pollsters are 99% confident that the result from this poll is off by fewer than 2.65 books from the actual average x.
i.e. E= 2.65
The confidence interval for population mean is given by :-
[tex]|\mu-x|\leq E[/tex]
Hence, the required inequality involving absolute value for : [tex]|15.7-x|\leq 2.65[/tex]
To solve this inequality for x, we have
[tex]\ 15.7-2.65\leq x\leq15.7+2.65\\\\\Rightarrow\ 13.05\leq x\leq18.35[/tex]
Hence, the interval in which the average is likely to fall :
[tex]13.05\leq x\leq18.35[/tex]
