The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. the manufacturer replaces free all motors that fail while under guarantee. if she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered? assume that the lifetime of a motor follows a normal distribution

The given are the following: Replacement = 3% or -1.88 from z-tables; Average Life = 10 years Standard Deviation = 2 years. 

Solution
Find how long a guarantee should be offered

10 years - 2 years * 1.88 = 6.24 years  or 75 months

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