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

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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.

Mathematics

1 answer:

irina [24] · Answer 1 · 2022-02-13T07:52:09+03:00

<h2>Answer with explanation:</h2>

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 :

$13.05\leq x\leq18.35$

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

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