While working in quality control, your job is to make sure that 95% of the 500 products which leave the factory each day are up to specifications. To test this, each day you select 25 products at random and check their quality. If no more than 1 product is poor quality, it is
While working in quality control, your job is to make sure that 95% of the 500 products which leave the factory each day are up to specifications. To test this, each day you select 25 products at random and check their quality. If no more than 1 product is poor quality, it is
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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Here is the scenario from week 6:
While working in quality control, your job is to make sure that 95% of the 500 products which leave the factory each day are up to specifications. To test this, each day you select 25 products at random and check their quality. If no more than 1 product is poor quality, it is considered acceptable. If 2 or more products are poor quality, you must test all 500 of the products manufactured that day, a costly and time-consuming process.
, the scenario with the quality control testing:
- Why can we not use the z scores associated with the probabilities in these sampling distributions to answer these questions? Be specific.
- Change the numbers in the scenario, to resolve the issue you just explained, and explain why these changes resolve the issue.
- Sketch the sampling distributions resulting from your changed numbers and rephrase the questions in terms of sampling distributions.
- Answer the questions in the scenario, with your new numbers, using the tools from this week for the sampling distribution of a sample proportion.
- Illustrate the answers to the questions on the graphs of the sampling distributions.
**Salamanders Again!**
For this portion, refer to the [Week 6 Collaborative SMP Assignment](#), the scenario with the salamanders:
- Describe the distribution of samples of size \( n = 100 \) from this population.
- Sketch this sampling distribution, and also sketch the distribution of salamander masses. Compare and contrast the two distributions.
- What is the probability of getting a sample of size \( n = 100 \) with mean \( \overline{X} < 7.2 \)? Explain your process.
- What is the probability of getting an individual salamander with a mass of \( X < 7.2 \) grams? Explain your process.
- Explain the difference between these two probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2F0b1c9b36-2c03-4d5b-a941-bca3e5a636c8%2Fq5xl7db_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Back in Quality Control!**
For this portion, refer to the [Week 6 Collaborative SMP Assignment](#), the scenario with the quality control testing:
- Why can we not use the z scores associated with the probabilities in these sampling distributions to answer these questions? Be specific.
- Change the numbers in the scenario, to resolve the issue you just explained, and explain why these changes resolve the issue.
- Sketch the sampling distributions resulting from your changed numbers and rephrase the questions in terms of sampling distributions.
- Answer the questions in the scenario, with your new numbers, using the tools from this week for the sampling distribution of a sample proportion.
- Illustrate the answers to the questions on the graphs of the sampling distributions.
**Salamanders Again!**
For this portion, refer to the [Week 6 Collaborative SMP Assignment](#), the scenario with the salamanders:
- Describe the distribution of samples of size \( n = 100 \) from this population.
- Sketch this sampling distribution, and also sketch the distribution of salamander masses. Compare and contrast the two distributions.
- What is the probability of getting a sample of size \( n = 100 \) with mean \( \overline{X} < 7.2 \)? Explain your process.
- What is the probability of getting an individual salamander with a mass of \( X < 7.2 \) grams? Explain your process.
- Explain the difference between these two probabilities.
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