Your firm has two plants, one large and one small, which mass produce a standard computer chip. Other than the amount they produce, the two plants are identical in all essential regards. Both use the same technology to produce the same product. When properly functioning, this technology produces 1% defective items. Whenever the number of defective items from one day's production exceeds 2%, a special note is made in the quality control log to flag the problem. At the end of the quarter, which plant would you expect to have more flagged days in the quality control log

This relates to the Law of Small numbers and how smaller samples are less likely to resemble the population that they are based on. Large samples on the other hand, are more able to resemble this population because they have more data.

In this case, the technology produces 1% defective items. The larger plant will therefore produce closer to 1% defective items on average than the smaller one because it is more likely to resemble the technology's parameters.

Look at it this way, the larger plant will produce more items so any defects will have a smaller percentage of the total as opposed to the Smaller plant.

For instance, the Small plant produces 100 items and the Large plant produces 200 items. Both of them each produce 2 defective items. For the large plant that will be 1% and for the small plant it would be 2%. Because the large plant has a higher production rate, it will report a lower percentage of defects on average.