Question

A poll found that a particular group of people read an average of 15.7 books per year. The pollsters are​ 99% confident that the result from this poll is off by fewer than 2.65 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 with explanation:

Given : A poll found that a particular group of people read an average of 15.7 books per year.

i.e. $\mu=15.7$

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 :-

$|\mu-x|\leq E$

Hence, the required inequality involving absolute​ value for  : $|15.7-x|\leq 2.65$

To solve this inequality for x, we have

$\ 15.7-2.65\leq x\leq15.7+2.65\\\\\Rightarrow\ 13.05\leq x\leq18.35$

Hence,  the interval in which the average is likely to fall :

$13.05\leq x\leq18.35$