Question

A book has 200 pages. The publisher claims that there are only 4% of error pages. An inspector takes a random selection of 20 pages as a sample. If x great or equal 2 error pages are found in a sample he will reject the book.

1. What distribution will you use? please formulate it (if you use an approximation please indicate and justify)
2. What is the rejection probability if what the publisher claimed (4%) is true?
3. What is the chance that the inspector accepts the book but it actually has 6% of error pages?

Answer 1

We have been given an event where there can be an error page or not and that the probability of being an error page is independent. So we can model it has binomial since there are only two possible outcomes.

n = 20 p= 4%

What distribution will you use? please formulate it (if you use an approximation please indicate and justify)

Binomial

P( X =x) =

We are not approximating since n < 30 and it is not large

What is the rejection probability if what the publisher claimed (4%) is true?

Rejection is when there 2 or more error pages in the sample. So the rejection probability will equal to probability of being 2 or more error pages

P(X > =2) = 1 - P( X < 2) ...........using complement rule

= 1 - [ P(X = 0) + P( X = 1) ]

= 1 - ()

= 1 - (0.442+0.3683)

P( rejection) = 0.1897

What is the chance that the inspector accepts the book but it actually has 6% of error pages?

Now we have p = 0.06

P( acceptance) = P( less than 2 are error)

= P( X = 0) + P(X= 1)

=

P(Acceptance) = 0.6605