start with multiplying z to each. you don't multiply it to the 6 because it is in the same parenthesis set, but you multiply it to everything in the other set. After multiplying, you get: , ,
now do that to the 6. After multiplying you get: , ,
now set it all next to each other + + + + +
now combine like terms. start with the to the highest power. since there is only one that has a third power, you put that one first. then you combine the squared ones, and so forth.
Find the rate of change, (y2-y1)/(x2-x1), from the data given...
(2.16-1.26)/(12-7)=0.18
(1.26-0.72)/(7-4)=0.18
Since the rate is constant, this is a linear equation of the form y=mx+b. Furthermore, since 0 pencils cost 0, b=0, so the cost of the pencils is simply the number of pencils times 18 cents...
c(p)=0.18p (cost with respect to pencils is 0.18 times the number of pencils)
Therefore, the correct interpolation of the confidence interval is that we are 99% confident that the true value of the population mean is between 0.328 and 0.486