Question

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.

          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.

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Added by Alex T.

Essentials of Modern Business Statistics

David R. Anderson, Dennis J.… 5th Edition

Chapter 5

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Solved by Expert Carolyn Behr-Jerome

08/03/2021

Step 1

Step 1: Identify what makes a binomial experiment A binomial experiment requires: 1) Fixed number of trials 2) Each trial has two possible outcomes (success/failure) 3) Probability of success remains constant for all trials 4) Trials are independent of each other Show more…

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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.

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00:01 So we're told that we have 3 % of the items that are being produced that are defective.

00:08 So we need to check if this is actually a binomial experiment.

00:12 So first of all, it's a binomial experiment if we have a fixed number of trials.

00:22 So in this case, we're only picking two parts, so that is fixed.

00:30 So check.

00:31 The second part is if the events are independent, and they are independent.

00:41 Picking one part isn't dependent on picking another.

00:46 And then the third criteria is that there are only two outcomes, and that is true too, because they're either defective or they're not defective.

00:56 So if 93 % are defective, that means 97 % are not.

01:03 Now, to make our tree diagram, we have two parts that we're picking.

01:12 So first part, i like to use slots, second part.

01:19 So on the first part, what are my potential outcomes? well, it can either be defective or not defective.

01:30 This probability is 0 .3.

01:32 This probability is 0 .7.

01:34 Now i pick my second part.

01:36 And with my second part, outcomes, are either defective or not defective.

01:41 Again, 0 .30 .70.

01:44 Now let's assume i get a non -defective.

01:46 Well, my second one could be defective or not defective.

01:53 So here's my true diagram...

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