A particular manufacturing design requires a shaft with a diameter of 17.000 mm, but shafts with diameters between 16.992 mm and 17.008 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 17.004 mm and a standard deviation of 0.004 mm. Complete parts (a) through (d) below. . For this process, what is the proportion of shafts with a diameter between 16.992 mm and 17.000 mm? The proportion of shafts with diameter between 16.992 mm and 17.000 mm is 0.1574 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 0.8400. Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 10% of the shafts? The diameter that will be exceeded by only 10% of the shafts is 17.0091 mm. Round to four decimal places as needed.) d. What would be your answers to parts (a) through (c) if the standard deviation of the shaft diameters were 0.003 mm? f the standard deviation is 0.003 mm, the proportion of shafts with diameter between 16.992 mm and 17.000 mm is 0.0918 Round to four decimal places as needed.) f the standard deviation is 0.003 mm, 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 17.000 mm, but shafts with diameters between 16.992 mm and 17.008 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 17.004 mm and a standard deviation of 0.004 mm. Complete parts (a) through (d) below. . For this process, what is the proportion of shafts with a diameter between 16.992 mm and 17.000 mm? The proportion of shafts with diameter between 16.992 mm and 17.000 mm is 0.1574 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 0.8400. Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 10% of the shafts? The diameter that will be exceeded by only 10% of the shafts is 17.0091 mm. Round to four decimal places as needed.) d. What would be your answers to parts (a) through (c) if the standard deviation of the shaft diameters were 0.003 mm? f the standard deviation is 0.003 mm, the proportion of shafts with diameter between 16.992 mm and 17.000 mm is 0.0918 Round to four decimal places as needed.) f the standard deviation is 0.003 mm, the probability that a shaft is acceptable is Round to four decimal places as needed.)
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter29: Tolerance, Clearance, And Interference
Section: Chapter Questions
Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...
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Transcribed Image Text:A particular manufacturing design requires a shaft with a diameter of 17.000 mm, but shafts with diameters between 16.992 mm and 17.008 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 17.004 mm and a
standard deviation of 0.004 mm. Complete parts (a) through (d) below.
a. For this process, what is the proportion of shafts with a diameter between 16.992 mm and 17.000 mm?
The proportion of shafts with diameter between 16.992 mm and 17.000 mm is 0.1574
(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 0.8400
(Round to four decimal places as needed.)
c. For this process, what is the diameter that will be exceeded by only 10% of the shafts?
The diameter that will be exceeded by only 10% of the shafts is 17.0091 mm.
(Round to four decimal places as needed.)
d. What would be your answers to parts (a) through (c) if the standard deviation of the shaft diameters were 0.003 mm?
If the standard deviation is 0.003 mm, the proportion of shafts with diameter between 16.992 mm and 17.000 mm is 0.0918
(Round to four decimal places as needed.)
If the standard deviation is 0.003 mm, the probability that a shaft is acceptable is
(Round to four decimal places as needed.)
G
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Step 1: Determine the given variables.
VIEWStep 2: Find the proportion.
VIEWStep 3: Find the proportion of acceptance.
VIEWStep 4: Find the value of diameter.
VIEWStep 5: Find the proportion of part ( a ) for a standard deviation of 0.003
VIEWStep 6: Find the proportion of part ( b ) for a standard deviation of 0.003
VIEWStep 7: Find the proportion of part ( c ) for a standard deviation of 0.003
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