1. When a machine is properly calibrated, 0.5% of its output is defective, but when it is out of adjustment, 6% of the output is defective. The technician in charge of calibration can successfully calibrate the machine in 90% of his attempts. The technician has just made an attempt to calibrate the machine.
a. What is the probability that the machine is in adjustment?
b. The first unit produced after the calibration effort is found to be defective. Given this information, what is the probability that the machine is in adjustment?
2. In examining borrower characteristics versus loan delinquency, a bank has collected the following informa- tion: (1) 15% of the borrowers who have been employed at their present job for less than 3 years are behind in their payments, (2) 5% of the borrowers who have been employed at their present job for at least 3 years are behind in their payments, and (3) 80% of the borrow- ers have been employed at their present job for at least 3 years. Given this information:
a. What is the probability that a randomly selected loan account will be for a person in the same job for at least 3 years who is behind in making payments?
b. What is the probability that a randomly selected loan account will be for a person in the same job for less than 3 years or who is behind in making payments?
c. If a loan account is behind, what is the probability that the loan is for a person who has been in the same job for less than 3 years?