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.
Step 1 of 3:
In this question, we are asked to find the probability that a randomly chosen book is more than 20.2 thick (not including the covers).
A - page book contains sheets of paper.
Thickness of paper has mean and standard deviation .
Let denote the thickness of the 250 sheets of paper.
We need to find
Now the sample size is , which is a large sample.
Then according to Central Limit Theorem,
Let be a simple random sample from a population with mean
and variance .
Let = be the total thickness.
Hence can be approximately normal distributed.
CLT specifies that and for sum of the sample items.
Hence we achieve,
Therefore we can write,
Now we will calculate the score because our distribution is approximately normal.
thus the score of 20.2 is
From the z table, the area to the left of is 0.8962.
Hence the area to the right is
= 1 - the area to the left of
= 1 - 0.8962
Hence the probability that a randomly chosen book is more than 20.2 thick is 0.1038.