Question

A manufacturer cuts shafts that fit into a valve hole. The design calls for the diameter of the shafts to be 22.000 mm. The process was found to produce shafts with a mean diameter of 22.002 and standard deviation of 0.005. What diameter will be exceeded by 2 percent of the shafts?

Answer 1

X ~ N ( µ = 22.002 , σ = 0.005 )
P ( X > x ) = 1 - P ( X < x ) = 1 - 0.02 = 0.98
To find the value of x
Looking for the probability 0.98 in standard normal table to calculate critical value Z = 2.0537
Z = ( X - µ ) / σ
2.0537 = ( X - 22.002 ) / 0.005
X = 22.0123
P ( X > 22.0123 ) = 0.02

Diameter will be exceeded by 2 percent of the shafts would be 22.0123 mm.