A television producer gurantees its TV for 3 years. On each TV, it makes a profit of 1500. But they must pay 5000 for any replacement under the gurantee. If this replacement also burns out within 3 years of purchase, they are not committed to a second replacement. Assume that the TV is normally distributed with a mean of 4.2 years and a stdv of 1.8 years

1) What is the expected profit per sale (net after paying for a possible replacement under the gurantee?

2) The producer wants to increase the expected profit per sale to 500 by reducing the period of gurantee.
What should be the probability in (a) in order to yeild the desired average profit?
To achieve the goal, what should be the period of gurantee?