Apoll 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.

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

i.e.

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 :-

Hence, the required inequality involving absolute value for  :

To solve this inequality for x, we have

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

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

where are the choices?