Question

Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain.

A company realizes that 5% of its pens are defective. In a package of 30 pens, is it likely that more than 6 are defective? Assume that pens in a package are independent of each other.

Group of answer choices

Yes

No. There are more than two possible outcomes.

No. 6 is more than 10% of 30

No, the chance of getting a defective pen changes depending on the pens that have already been selected.

No. The pens in a package are dependent on each other.

Answer 1

Solution: The correct answer is: Yes

Explanation: The probability based on Bernoulli trials should satisfy the following properties:

1. There are a fixed number of trials under consideration.

2. There are only two possible outcomes associated with each trail.

3. The probability of success remains the same across all the trails.

4. The outcomes of each trial are independent of each other.

Now, let's see if these properties are satisfied;

The given random experiment consists of a package of 30 pens. Therefore, the number of trails is 30.

There are two outcomes associated with each trail. That is, either a pen is defective or non-defective.

The probability of defective remains same across all the 30 trails and it is 0.05.

The pens in a package are independent of each other is the given condition.

Therefore, all the conditions required for the Bernoulli trails are satisfied. Therefore, the given probability model is based on the Bernoulli trials.