## Quality Control

1.2.1. Sampling without Replacement

As a second example, consider the following case. Suppose you are in charge of quality control in a light bulb factory. Each day N light bulbs are produced. But before they are shipped out to the retailers, the bulbs need to meet a minimum quality standard such as not allowing more than R out of N bulbs to be defective. The only way to verify this exactly is to try all the N bulbs out, but that will be too costly. Therefore, the way quality control is conducted in practice is to randomly draw n bulbs without replacement and to check how many bulbs in this sample are defective.

As in the Texas lotto case, the number M of different samples Sj of size n you can draw out of a set of N elements without replacement is

Each sample Sj is characterized by ...

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