A 500-page book contains 250 sheets of paper. The

Step 1 of 3 

(a)

In this question, we are asked to find the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers).

A 500 - page book contains 250 sheets of paper.

Thickness of paper has mean 0.08 mm and standard deviation 0.01 mm .

Let , denote the thickness of the 250 sheets of paper.

We need to find P(X > 20.2).

Now the sample size is n = 250 , 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,

Mean  

Variance

         = 250

 =

Standard deviation

Therefore we can write,

Now we will calculate the Z score because our distribution is approximately normal.

thus the Z score of 20.2 mm is

    =  

    =

  z = 1.265

From the z table, the area to the left of 1.265 is 0.8962.

Hence the area to the right is

P(X > 20.2) = 1 - the area to the left of 1.265

P(X > 20.2) = 1 - 0.8962

P(X > 20.2) = 0.1038

Hence the probability that a randomly chosen book is more than 20.2 mm thick is 0.1038.