A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error. Suppose that the company selects a random sample of 400 pages and finds 33 that have an error. If the printer is meeting the standard, what is the probability that a sample of this size would have 33 or more errors?
A) 0.0014
B) 0.4986
C) 0.9986
D) 0.1245
E) 0.3755

Question

Quizplus · Accepted Answer

This is a problem that can be solved using the binomial or normal approximation to the binomial distribution. Given that the standard is no more than 5% of the pages should have errors, and a sample of 400 pages is taken, we expect 20 pages (5% of 400) to have errors under the standard. Finding 33 errors in a sample of 400 suggests a higher error rate than the standard. Using the normal approximation to the binomial distribution (because the sample size is large), we calculate the probability of observing 33 or more errors if the true error rate is 5%. The result is a low probability (0.0014), indicating that observing 33 or more errors is highly unlikely if the printer is meeting the standard, thus suggesting the printer might not be meeting the specified error rate.

A Major Textbook Publisher Has a Contract with a Printing