X = life of motor

x = guarantee period

Normal Curve: μ = 10, σ = 2

We need to find the value (in years) that will give us the bottom 3% of the distribution. These are the motors that we are willing to replace under the guarantee.

P(X < x) = 0.03

The area that we can find from the z-table is

0.5 - 0.03 = 0.47

The corresponding z-score is z = -1.88.

Since , we can write:

Solving this gives x = 6.24.

So the guarantee period should be 6.24 years.