A particular manufacturing design requires a shaft with adiameter of 17.000 ​mm, but shafts with diameters between 16.988 mmand 17.012 mm are acceptable. The manufacturing process yieldsshafts with diameters normally​ distributed, with a mean of 17.004mm 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 adiameter between 16.988mm and 17.000 mm​?
The proportion of shafts with diameter between 16.988 mm and17.000 mm is 0.1587.
​(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 0.9772.
​(Round to four decimal places as​ needed.)
c. For this​ process, what is the diameter that will be exceededby only 2.5​% of the​ shafts?
The diameter that will be exceeded by only 2.5​% of the shaftsis 17.0118 mm.
​(Round to four decimal places as​ needed.)
d. What would be your answers to parts​ (a) through​ (c) if thestandard deviation of the shaft diameters were 0.003 ​mm? If thestandard deviation is 0.003​mm, the proportion of shafts withdiameter between 16.988 mm and 17.000 mm is
