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

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

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(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(x - 10)/(2))=0.03`

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

`P(z<-1.881) = 0.03`

`\displaystyle(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.