A large mail house which mails such items as catalogues,magazines,and other bulk mailings guarantees that there will be no more than a 3% error rate on its mailing labels.A customer who contracted a mailing to 190,000 individuals experienced a return of 5,900 items,which had incorrect addresses.Which of the following statements is true?
A) There is a 3% chance of an incorrect return.
B) There is a 0.0054 probability that a return of 5900 or more incorrect addresses could occur if the true error rate is 3%.
C) There is a 0.4964 probability that a return of 5900 or more incorrect addresses could occur if the true error rate is 3%.
D) There is a 2.69 percent possibility that a return of 5900 incorrect addresses could occur if the true error rate is 3%.
E) None of these statements are correct.

Question

Quizplus · Accepted Answer

The probability of getting 5900 or more incorrect addresses can be calculated using the binomial distribution. The probability of getting x incorrect addresses out of n mailings if the true error rate is p is given by:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where (n choose x) is the binomial coefficient.

In this case, n = 190000, p = 0.03, and x = 5900. Using a calculator or software tool, we can find that P(x ≥ 5900) = 0.0054. This means that there is a 0.54% chance of getting 5900 or more incorrect addresses if the true error rate is 3%. Therefore, statement B is true. None of the other statements are correct.

A Large Mail House Which Mails Such Items as Catalogues,magazines,and