Defective CDs

A manufacturer of CDs has two plants. Last month one plant made 156,429 CDs, of which 4,280 were defective. At the other plant, 2-1/2 percent of the 325,143 CDs made last month were defective. Which plant did better?

Approaches

The percent at the first plant is about 2.74% That's better than the 2-1/2 percent at the second plant. So the first plant is doing better. The 325,143 is irrelevant.

response

The 325,143 is relevant. 2-1/2 percent of 325,143 is more than 4280, so the first plant is doing better.

response

325,143 is relevant, but not for that reason. The higher percent of a larger volume is expected.

ratios

savings from buying in quantity, more efficiency in larger plant may compensate for larger rate of defects. What do we mean by "better"?

Your experience

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

Last updated 30 November, 2004