A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has a mean of 0.08 mm and a standard deviation of 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.

Step-by-step explanation:

a. Let X be paper. the thickness .

Given the paper's parameters  

-Also, let S be the book's thickness.

The book's parameters are calculated as:

# the probability that a randomly chosen book is more than 20.2 mm thick is then calculated as:

Hence, the probability is 0.103 or 10.3%

b. let's denote the 10th percentile as , for the book's thickness.

From a above, we have the mean for the book's thickness as and the variance as .

#We therefore calculate the 10th percentile as;

Hence,  the 10th percentile of the book's thickness is 19.797 mm

c.No.

-This is because the distribution of the book's thickness is not known.

-Hence, this probability cannot be calculated.

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step-by-step explanation: