(d) Compute the probabilities associated with finding no defects, exactly one defect, and two defects. (Round your answers to four decimal places.) P(no defects) = 0.9410 x P(1 defect) = 0.0582 P(2 defects) = 0.0009
(d) Compute the probabilities associated with finding no defects, exactly one defect, and two defects. (Round your answers to four decimal places.) P(no defects) = 0.9410 x P(1 defect) = 0.0582 P(2 defects) = 0.0009
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer step d.
![**Transcription for Educational Website**
---
**Problem Description:**
When a new machine is functioning properly, only 7% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and are interested in the number of defective parts found.
(a) **Binomial Experiment Conditions:**
To determine the conditions under which this situation would be a binomial experiment, consider the following (select all that apply):
- [x] The parts must be selected independently.
- [ ] The probability of choosing a part that is defective must be 0.93.
- [ ] The selection of a part is dependent on the first part selected.
- [x] For each part selected, the probability of a defective part being produced must be 0.07.
- [ ] The number of successes and failures in this experiment are equal.
(b) **Tree Diagram:**
The following diagram represents the problem as a two-trial experiment:
- **Tree Diagram Overview**
1. Start at the root node.
2. Branch 1: "Defective"
- Sub-branch 1: "Defective, Defective" (both parts are defective)
- Sub-branch 2: "Defective, Not Defective" (first part defective, second part not defective)
3. Branch 2: "Not Defective"
- Sub-branch 1: "Not Defective, Defective" (first part not defective, second part defective)
- Sub-branch 2: "Not Defective, Not Defective" (both parts are not defective)
Each path in the tree corresponds to a possible outcome of the selection process, illustrating all combinations of defective and non-defective parts in a two-part sample.
**Relevant Visuals**: The tree diagram visually represents these trials, showing paths for each scenario and ensuring clarity in identifying outcomes.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9522b0ac-6bb6-4104-840b-2a5d14259dd3%2Ffc5b71ae-85b0-474e-8081-d785f6777bf9%2F4wgp0a9_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
---
**Problem Description:**
When a new machine is functioning properly, only 7% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and are interested in the number of defective parts found.
(a) **Binomial Experiment Conditions:**
To determine the conditions under which this situation would be a binomial experiment, consider the following (select all that apply):
- [x] The parts must be selected independently.
- [ ] The probability of choosing a part that is defective must be 0.93.
- [ ] The selection of a part is dependent on the first part selected.
- [x] For each part selected, the probability of a defective part being produced must be 0.07.
- [ ] The number of successes and failures in this experiment are equal.
(b) **Tree Diagram:**
The following diagram represents the problem as a two-trial experiment:
- **Tree Diagram Overview**
1. Start at the root node.
2. Branch 1: "Defective"
- Sub-branch 1: "Defective, Defective" (both parts are defective)
- Sub-branch 2: "Defective, Not Defective" (first part defective, second part not defective)
3. Branch 2: "Not Defective"
- Sub-branch 1: "Not Defective, Defective" (first part not defective, second part defective)
- Sub-branch 2: "Not Defective, Not Defective" (both parts are not defective)
Each path in the tree corresponds to a possible outcome of the selection process, illustrating all combinations of defective and non-defective parts in a two-part sample.
**Relevant Visuals**: The tree diagram visually represents these trials, showing paths for each scenario and ensuring clarity in identifying outcomes.
---
Transcribed Image Text:(d) Compute the probabilities associated with finding no defects, exactly one defect, and two defects. (Round your answers to four decimal places.)
P(no defects) = 0.9410 ❌
P(1 defect) = 0.0582 ❌
P(2 defects) = 0.0009 ❌
Each probability is followed by a red cross, indicating that the provided answers are incorrect.
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