Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 14 years and a standard deviation of 2 years.

Question

If the company wants to provide a warranty so that only 1.3% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?

warranty = ____years

What does the percentage represent? Also how would I use a z-table/score to solve for this equation?

Answer 1

Hi Persius, the percentage represents the portion of the normal curve that is less than the warranty cutoff the company wants to set.

To find the corresponding z-score, first convert it to a decimal: 1.3% = 0.013.

Now, go to your table of z-values and look for the p-value that is as close to 0.013 that you can find. Remember, the p-values are the values in the middle of the table.

You should find that the corresponding z-score is -2.23.

Now, to find the warranty cutoff, apply the boundary-finding formula:

x = µ + zσ

x = (14) + (-2.23)(2)

x = 9.54 years.

Does that all make sense?