Question

The average life of a certain type of small motor is 10 years with a side of 2 yrs. The manufacturer replaces free all motors that fail while under guarantee. If he is willing to replace only 3% of the motors that fail how long a guarantee should be offer? Assume that the lifetime ofa motor follows normal distribution.

Answer 1

We have that $\mu=10, \sigma=2$

$P(X\leq x)=P(Z\leq \frac{x-\mu}{\sigma})=0.03$

Z-value of –1.88 to 3% of area under the curve. Then

$\frac{x-\mu}{\sigma}=\frac{x-10}{2}=-1.88$

Solve for x

$x=10-2\cdot1.88=6.24$

Answer: 6.24 years.