Question

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?

Answer 1

Answer:

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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(X<x) = 0.03

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

P(X < x)  

$P( X < x) = P( z < \displaystyle\frac{x - 10}{2})=0.03$  

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

$P(z$

$\displaystyle\frac{x - 10}{2} = -1.881\\x = 6.238$  

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