When a new machine is functioning properly, only 4% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found. (a) Describe the conditions under which this situation would be a binomial experiment. (Select all that apply.) For each part selected, the probability of a defective part being produced must be 0.04. The number of successes and failures in this experiment are equal. The probability of choosing a part that is defective must be 0.96. The parts must be selected independently. The selection of a part is dependent on the first part selected.

Question

Emerson Burns

Mathematics

27 June, 10:51

When a new machine is functioning properly, only 4% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found. (a) Describe the conditions under which this situation would be a binomial experiment. (Select all that apply.) For each part selected, the probability of a defective part being produced must be 0.04. The number of successes and failures in this experiment are equal. The probability of choosing a part that is defective must be 0.96. The parts must be selected independently. The selection of a part is dependent on the first part selected.

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Answers (1)

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Samuel Henderson · Answer 1

For each part selected, the probability of a defective part being produced must be 0.04.

The parts must be selected independently.

Step-by-step explanation:

For each part, there are only two possible outcomes. Either they are defective, or they are not. Each part has a 4% probability of being defective, and the probability of a part being defective is independent of other parts, that is, they are selected independently. These are the conditions under which this situation would be a binomial experiment.

So the correct answers are:

For each part selected, the probability of a defective part being produced must be 0.04.

The parts must be selected independently.