Question

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.

Answer 1

Answer 2

Let life be denoted by the variable X

So

P(X

So

P(Z<(a-10)/2)=0.03

So

1-P(Z<(10-a)/2)=0.03

So

P(Z<(10-a)/2)=0.97

So

(10-a)/2=1.88

So

a=6.24 years must be the guarantee to be given