Question: An operator needs to produce 4 pins and 6 shafts using a lathe which has 72% chance of producing a defect-free pin at each trial and 65% chance of producing a defect-free shaft at each trial. The operator will first produce pins one by one until he has 4 defect-free pins and then produce shafts one by one until he has 6 defect-free shafts.
a. What is the expected value and variance of the total number of trials that the operator will make?
b. Suppose each trial for pins takes 12 minutes and each trial for shafts takes 25 minutes. What is the expected value and variance of the total time required?