Question

Quality control studies for Speedy Jet Computer Printers show the lifetime of the printer follows a normal distribution with mean = 4 years and standard deviation = 0.78 years. The company will replace any printer that fails during the guarantee period. How long should Speedy Jet printers be guaranteed if the company wishes to replace no more than 10% of the printers?

Answer 1

Answer:

About 3 years Speedy Jet printers be guaranteed.

Step-by-step explanation:

Given : Quality control studies for Speedy Jet Computer Printers show the lifetime of the printer follows a normal distribution with

mean $\mu = 4$ and standard deviation  $\sigma = 0.78$

If the company wishes to replace no more than 10% of the printers.

To find : How long should Speedy Jet printers be guaranteed ?

Solution :

Using Z- table,  

Z value corresponding to 10% or 0.10 = -1.28.

Applying z-score formula,

$z=\frac{x-\mu}{\sigma}$

The value of x is given by,

$x=(z\times \sigma)+\mu$

Substitute the values,

$x=(-1.28\times 0.78)+4$

$x=-0.9984+4$

$x=3.0016$

So, approx 3 years.

Therefore, About 3 years Speedy Jet printers be guaranteed.