Question

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 deviation0.01mm. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)

Answer 1

Answer:

Probability = 0.1038 or 10.38%

Step-by-step explanation:

Given,

Number of sheets n = 250

Mean $\mu =0.08$

Standard deviation $\sigma =0.01$

$S_{n}$ = Sum of sample items.

From the Central Limit Theorem we get, $S_{n}$~$N(n\mu ,n\sigma^2)$

n\mu = 250 × 0.08

        = 20

$\sigma^2S_{n}=n\sigma^2$

        = 250(0.01)²

        = 0.025

Therefore, $S_{n}$~N(20,0.025)

The Z-value corresponding to 20.2 :

$Z=\frac{20.2-20}{\sqrt{0.025}}$

= 1.26

Finally, $P(S_{n}>20.2)=P(z>1.26)$

                                  = 1 - 0.8962

                                  = 0.1038

Probability = 0.1038 or 10.38%