A company produces refrigerator motors. These engines have alife expectancy of 19.4 years with a standard deviation of 4.8years. Assume that the service life of the motors is normallydistributed.

a) Calculate the probability of an engine operating for lessthan 12 years.
Calculate the probability of an engine operating for more than 25years.
Calculate the probability that the life of an engine is between 10and 20 years.

In order to promote the sale of their engines, the company wantsto issue a guarantee on the engines which means that the customercan replace the engine free of charge if it breaks before a certaintime.

b) How many years of warranty can the company expire if they donot want to replace more than 2.5% of the engines? (That is, thewarranty period should be such that the probability that anengine's service life is less than the warranty period is0.025)
The company has a profit of NOK 1200 on a motor that does not failbefore the warranty period, while it has a loss of NOK 4500 (ie aprofit of -4500 kroner) on a motor that fails before the warrantyperiod. If the company uses the warranty period calculated, what isthe expected profit from the sale of an engine?
Briefly explain what this expected profit in practice tells us.