A particular manufacturing design requires a shaft with a diameter between 20.92

Question

A particular manufacturing design requires a shaft with a diameter between 20.92 mm and 21.010 mm. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.003 mm and a standard deviation of 0.005 mm. Complete parts (a) through (c) a. For this process what is the proportion of shafts with a diameter between 20.92 mm and 21.00 mm? The proportion of shafts with diameter between 20.92 mm and 21.00 mm is (Round to four decimal places as needed.) b. For this process what is the probability that a shaft is acceptable? The probability that a shaftis acceptable is (Round to four decimal places as needed.) C. For this process what is the diameter that will be exceeded by only 2.5% of the shafts? The diameter that will be exceeded by only 2.5% of the shafts is[]mm. Round to four decimal places as needed.) 13

Explanation / Answer

Ans:

a)

z=(20.92-21.003)/0.005=-16.6

z=(21.00-21.003)/0.005=-0.6

P(-16.6<z<-0.6)=P(z<-0.6)-P(z<-16.6)=0.2743-0=0.2743

b)

z=(21.01-21.003)/0.005=1.4

P(-16.6<z<1.4)=P(z<1.4)-P(z<-16.6)=0.9192

c)

P(Z>z)=0.025

P(Z<=z)=1-0.025=0.975

z=1.96

x=21.003+1.96*0.005=21.0128

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