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A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.990 mm and 21.010 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.005 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 20.990 mm and 21.000 mm? The proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1961. (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 0.7915. (Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 0.5% of the shafts? The diameter that will be exceeded by only 0.5% of the shafts is 21.0205 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 0.005 mm? If the standard deviation is 0.005 mm, the proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1573'. (Round to four decimal places as needed.) If the standard deviation is 0.005 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 21.000 mm, but shafts with diameters between 20.990 mm and 21.010 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.005 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 20.990 mm and 21.000 mm? The proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1961. (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 0.7915. (Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 0.5% of the shafts? The diameter that will be exceeded by only 0.5% of the shafts is 21.0205 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 0.005 mm? If the standard deviation is 0.005 mm, the proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1573'. (Round to four decimal places as needed.) If the standard deviation is 0.005 mm, the probability that a shaft is acceptable is (Round to four decimal places as needed.)

Mathematics For Machine Technology
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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A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.990 mm and 21.010 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.005 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 20.990 mm and 21.000 mm? The proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1961 . (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 0.7915. (Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 0.5% of the shafts? The diameter that will be exceeded by only 0.5% of the shafts is 21.0205 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 0.005 mm? If the standard deviation is 0.005 mm, the proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1573'. (Round to four decimal places as needed.) If the standard deviation is 0.005 mm, the probability that a shaft is acceptable is (Round to four decimal places as needed.)
Transcribed Image Text:A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.990 mm and 21.010 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.005 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 20.990 mm and 21.000 mm? The proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1961 . (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 0.7915. (Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 0.5% of the shafts? The diameter that will be exceeded by only 0.5% of the shafts is 21.0205 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 0.005 mm? If the standard deviation is 0.005 mm, the proportion of shafts with diameter between 20.990 mm and 21.000 mm is 0.1573'. (Round to four decimal places as needed.) If the standard deviation is 0.005 mm, the probability that a shaft is acceptable is (Round to four decimal places as needed.)
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