Question

In each situation below, is it reasonable to use a binomial model to solve the problem? If your answer is no, give reasons for your answer. If a binomial distribution applies, define the random variable involved and the two parameters, n and p.

e. A company realizes that about 10% of its packages are not being sealed properly. In a case of 24, what is the probability that more than 3 are unsealed?

Answer 1

It is reasonable to use a binomial model for the company's unsealed packages, with a binomial distribution counting the number of unsealed packages as the random variable X, n = 24 trials, and a success probability p = 0.10.

Step-by-step explanation:

Yes, it is reasonable to use a binomial model to solve the problem regarding the company's unsealed packages. The scenario fits the criteria for a binomial distribution because there is a fixed number of trials (n = 24 packages), there are only two possible outcomes (a package is sealed properly or it is not), and each package being sealed properly is independent of the others, assuming the company's machinery or process does not change during the sealing of the 24 packages. The probability of a package not being sealed properly (success in this context) is p = 0.10, and the probability of a package being sealed properly (failure in this context) is q = 1 - p = 0.90. The random variable X would represent the number of unsealed (not sealed properly) packages.

The specific question to be answered is the probability that more than three packages are not sealed properly, which can be found by calculating 1 minus the probability of three or fewer packages being unsealed.