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 …

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asked Oct 24, 2020 228k views

1 Answer

Onedayitwillmake · Answer 1 · 2020-10-29T17:32:55+0000

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 :

$13.05\leq x\leq18.35$