A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.991 mm and 21.009 mm are acceptable. The manufacturing process yields shafts with dianmeters normally distributed, with a mean of 21.002 mm and a standard deviation of 0.006 mm. Complete parts (a) through (d) below. ..... a. For this process, what is the proportion of shafts with a diameter between 20.991 mm and 21.000 mm? The proportion of shafts with diameter between 20.991 mm and 21.000 mm is 3371. (Round to four decimal places as needed.) b. For this process, what is the probability that a shaft is acceptable? The probability that a shaft is acceptable is. (Round to four decimal places as needed.)
A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.991 mm and 21.009 mm are acceptable. The manufacturing process yields shafts with dianmeters normally distributed, with a mean of 21.002 mm and a standard deviation of 0.006 mm. Complete parts (a) through (d) below. ..... a. For this process, what is the proportion of shafts with a diameter between 20.991 mm and 21.000 mm? The proportion of shafts with diameter between 20.991 mm and 21.000 mm is 3371. (Round to four decimal places as needed.) b. For this process, what is the probability that a shaft is acceptable? The probability that a shaft is acceptable is. (Round to four decimal places as needed.)
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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![**Educational Content: Understanding Shaft Diameter in Manufacturing**
A particular manufacturing design requires a shaft with a diameter of 21.000 mm. However, shafts with diameters between 20.991 mm and 21.009 mm are considered acceptable. The manufacturing process yields shafts with diameters that are normally distributed, having a mean of 21.002 mm and a standard deviation of 0.006 mm.
### Exercises:
**a. Proportion of Shafts with Diameters between 20.991 mm and 21.000 mm**
- **Question:** For this process, what is the proportion of shafts with a diameter between 20.991 mm and 21.000 mm?
- **Answer:** The proportion of shafts with diameters between 20.991 mm and 21.000 mm is 0.3371. *(Round to four decimal places as needed.)*
**b. Probability of Acceptable Shafts**
- **Question:** For this process, what is the probability that a shaft is acceptable?
- **Answer:** The probability that a shaft is acceptable is [ ]. *(Round to four decimal places as needed.)*
This exercise illustrates how to determine acceptable deviations in part dimensions based on normal distribution in manufacturing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F108f85ec-5786-44dd-b590-51bf325bef20%2F89b8f754-3cb2-4abf-b341-d31c552947e8%2Fyouq3bq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Understanding Shaft Diameter in Manufacturing**
A particular manufacturing design requires a shaft with a diameter of 21.000 mm. However, shafts with diameters between 20.991 mm and 21.009 mm are considered acceptable. The manufacturing process yields shafts with diameters that are normally distributed, having a mean of 21.002 mm and a standard deviation of 0.006 mm.
### Exercises:
**a. Proportion of Shafts with Diameters between 20.991 mm and 21.000 mm**
- **Question:** For this process, what is the proportion of shafts with a diameter between 20.991 mm and 21.000 mm?
- **Answer:** The proportion of shafts with diameters between 20.991 mm and 21.000 mm is 0.3371. *(Round to four decimal places as needed.)*
**b. Probability of Acceptable Shafts**
- **Question:** For this process, what is the probability that a shaft is acceptable?
- **Answer:** The probability that a shaft is acceptable is [ ]. *(Round to four decimal places as needed.)*
This exercise illustrates how to determine acceptable deviations in part dimensions based on normal distribution in manufacturing.
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