Question

Quality control for Lexmark Printers shows the lifetime of the printer follows a normal distribution with mean μ=6.78 years and standard deviation σ=.86 years. The company will replace any printer that fails during the guarantee period. How long should Lexmark Printers be guaranteed if the company wishes to replace no more than 18% of the printers?

Answer 1

Using z-scores and the normal distribution, we can determine the guarantee period Lexmark Printers should offer to ensure that no more than 18% of printers are replaced under the warranty.

Step-by-step explanation:

The question falls under the field of statistics, a branch of mathematics, and deals with establishing a guarantee period based on a normal distribution of product life expectancy. To determine how long Lexmark Printers should be guaranteed if the company wishes to replace no more than 18% of the printers, we can use the concept of z-scores in a normal distribution. Given the mean (μ) life of a printer is 6.78 years and the standard deviation (σ) is 0.86 years, we look for the z-score that corresponds to the 82nd percentile (100% - 18%) in a standard normal distribution table.

First, we calculate the z-score using the formula: z = (X - μ) / σ. We then look up this z-score in a standard normal distribution table (or use a calculator) to find the value of X that corresponds to the 82nd percentile. This X value will be the guarantee period Lexmark should offer to limit replacements to 18% of the printers.