 # When a new machine is functioning properly, only 3% 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. b. Draw a tree diagram similar to Figure 5.4 showing this problem as a two-trial experiment. c. How many experimental outcomes result in exactly one defect being found? d. Compute the probabilities associated with finding no defects, exactly one defect, and two defects. 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section
Chapter 5.5, Problem 36E
Textbook Problem
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## When a new machine is functioning properly, only 3% 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. b. Draw a tree diagram similar to Figure 5.4 showing this problem as a two-trial experiment. c. How many experimental outcomes result in exactly one defect being found? d. Compute the probabilities associated with finding no defects, exactly one defect, and two defects.

Expert Solution

a.

To determine

Explain the conditions under which the given situation will be a binomial experiment.

### Explanation of Solution

Calculation:

It was found that only 3% of the items produced are defective when the new machine is functioning properly. One is interested in the defective parts which are randomly selected from the two parts that are produced from the machine

Criteria for binomial distribution:

• Each experiment has fixed number of trials.
• Each trial is independent of the other.
• There are two possible outcomes. That are success and failure.
• Probability of success is same for all trials.

Define the random variable x as the number of defective parts found. Two parts produced on the machine are selected randomly...

Expert Solution

b.

To determine

Draw a tree diagram representing the problem as a two trial experiment.

Expert Solution

c.

To determine

Find the number of outcomes that results exactly one defective.

Expert Solution

d.

To determine

Find the probability that there is no defective, exactly one defective and two defective.

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