Question

A company produces refrigerator motors. These engines have a life expectancy of 19.4 years with a standard deviation of 4.8 years. Assume that the service life of the motors is normally distributed. a) Calculate the probability of an engine operating for less than 12 years. Calculate the probability of an engine operating for more than 25 years. Calculate the probability that the life of an engine is between 10 and 20 years. In order to promote the sale of their engines, the company wants to issue a guarantee on the engines which means that the customer can replace the engine free of charge if it breaks before a certain time. b) How many years of warranty can the company expire if they do not want to replace more than 2.5% of the engines? (That is, the warranty period should be such that the probability that an engine's service life is less than the warranty period is 0.025) The company has a profit of NOK 1200 on a motor that does not fail before the warranty period, while it has a loss of NOK 4500 (ie a profit of -4500 kroner) on a motor that fails before the warranty period. If the company uses the warranty period calculated, what is the expected profit from the sale of an engine? Briefly explain what this expected profit in practice tells us.

          A company produces refrigerator motors. These engines have a
life expectancy of 19.4 years with a standard deviation of 4.8
years. Assume that the service life of the motors is normally
distributed.
a) Calculate the probability of an engine operating for less
than 12 years.
Calculate the probability of an engine operating for more than 25
years.
Calculate the probability that the life of an engine is between 10
and 20 years.
In order to promote the sale of their engines, the company wants
to issue a guarantee on the engines which means that the customer
can replace the engine free of charge if it breaks before a certain
time.
b) How many years of warranty can the company expire if they do
not want to replace more than 2.5% of the engines? (That is, the
warranty period should be such that the probability that an
engine's service life is less than the warranty period is
0.025)
The company has a profit of NOK 1200 on a motor that does not fail
before the warranty period, while it has a loss of NOK 4500 (ie a
profit of -4500 kroner) on a motor that fails before the warranty
period. If the company uses the warranty period calculated, what is
the expected profit from the sale of an engine?
Briefly explain what this expected profit in practice tells us.

Added by Thomas S.

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