In a certain factory, some machines are properly adjusted and some need adjusting. Technicians randomly inspect machines and make adjustments. Suppose that, of the machines that are properly adjusted on a particular day, 80% will also be properly adjusted the following day and 20% will need adjusting. Also, of the machines that need adjusting on a particular day, 30% will be properly adjusted the next day and 70% will still need adjusting.
(a) Set up the 2 × 2 stochastic matrix, with columns labeled P (properly adjusted) and N (need adjusting), that describes this situation.
(b) If, initially, all the machines are properly adjusted, what percent will need adjusting after 2 days?
(c) In the long run, what percent will be properly adjusted each day?