A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and standard deviation 0.01 mm.
a. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)?
b. What is the 10th percentile of book thicknesses?
c. Someone wants to know the probability that a randomly chosen page is more than 0.1 mm thick. Is enough information given to compute this probability? If so, compute the probability. If not, explain why not.
(a) Let 
denote the thicknesses of the 250 sheets of paper.
Let 
be the total thickness of the 250 pages.
Then S is approximately normally distributed with mean 
The z-score of 20.2 is (20.2 ? 20)/0.158114 = 1.26.
The area to the right of z = 1.26 is 1 ? 0.8962 = 0.1038.
P(S>20.2)=0.1038.
(b) Let 
denote the 10th percentile
The z-score of the 10th percentile is approximately z=?1.28.
Therefore satis?es the equation 
.
= 19.798mm.
(c) No, because we don’t know the distribution of page thicknesses. In particular, we do not know whether the page thicknesses are normally distributed.
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