The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. the manufactorer 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?

If the average life is less than 6.24 years, then, it lies in the lower 3% and willing to be replaced.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 10

Standard Deviation, σ = 2

We assume that the distribution of average life is a bell shaped distribution that is a normal distribution.

Formula:

a) P(X<x) = 0.03

We have to find the value of x such that the probability is 0.03.

P(X < x)  

Calculation the value from standard normal z table, we have,  

Hence, if the average life is less than 6.24 years, then, it lies in the lower 3% and willing to be replaced.