Statistical Tolerance

A mass-produced product assembled by a random selection two identical components A1 and A2 and fitting them into a slot in B. The machine producing the slot in B is maintained in statistical control with a mean slot width of 33.55 mm and a standard deviation of 0.2 mm. The process producing A1 and A2 can also be kept in control at a desired mean value and a standard deviation of 0.05 mm. Assuming the data is normally distributed, determine the following:

a) Assuming a minimum clearance of 0.30 mm is required, what must be the mean for the process producing A1 and A2 if no more than 10% of the assemblies can have a clearance less than this value?

b) What maximum clearance might occasionally be found with a chance of 1 in 1000?

c) During assembly, will there be cases for which there is no clearance? If so, what will be the expected percentage?