  ### Home > INT3 > Chapter 6 > Lesson 6.2.3 > Problem6-54

6-54.

A copy machine company advertises that its copiers will make at least $25,000$ copies before requiring maintenance. A consumer research group tested the claim by collecting repair data for that model of copy machine in $40$ different regions of the country. The means of the numbers of copies made before the copier needed maintenance for each of the $40$ regions have been sorted and are listed in the table below.

 $24551$ $24656$ $24764$ $24889$ $24928$ $24574$ $24656$ $24767$ $24893$ $25020$ $24600$ $24691$ $24782$ $24895$ $25024$ $24609$ $24705$ $24791$ $24904$ $25025$ $24612$ $24717$ $24793$ $24910$ $25028$ $24615$ $24725$ $24796$ $24911$ $25033$ $24618$ $24735$ $24798$ $24914$ $25041$ $24652$ $24758$ $24883$ $24928$ $25249$ checksum $992,440$

What are the upper and lower $5$$\%$ bounds of the sample-to-sample variability? Predict the number of copies that can be made before a machine requires maintenance. Do you think the consumer research group will dispute the company’s claim?

There are $40$ data points. Which data points can be used for $5$$\%$ and $95$$\%$?