Supposes that the diameter of bearings are independent normally distributed random variables with mean µB = 1.005cm and variance σ²B = (0.003)² cm² . The diameter of shafts are independent normally distributed random variables having mean µB = 0.995cm cm and variance σ²s = 0.004² (cm²) .
a) What is the probability Pr(S > B) of interference?
b) What is the probability of one or fewer interferences in 20 random shaft-bearing pairs?
The clearance, defined by C = B - S, is normally distributed (why?) and interference occurs only if C < 0.