CPM Homework Help : INT3 Problem 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?

Hint:

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