United Refrigerator ( UE ) sells refrigerators for $ 400 with one- year warranty . The warranty works as follows : If any part of the refrigerator fails during the first year after purchase , VE replaces the refrigerator for an average cost of $ 100 . As soon as a replacement is made another one year warranty begins for the customer . If the refrigerator fails outside of the warranty period , we assume the customer immediately purchases another UE refrigerator . Suppose that the amount of time that a refrigerator lasts follows a normal distribution with a mean 1 8 years and a standard deviation of .3 year 1 ) Estimate the profit that UE can earn from a customer during a year 2 ) How could the approach be used to determine the optimal warranty period