The problem asks us to identify the population and sample in a given scenario. The librarians are interested in the number of books and media checked out by patrons. They examine the checkout records of $150$ randomly selected adult patrons.

1. Problem Description

The problem asks us to identify the population and sample in a given scenario. The librarians are interested in the number of books and media checked out by patrons. They examine the checkout records of $150$ randomly selected adult patrons.

2. Solution Steps

The population is the entire group that we are interested in studying. The sample is a subset of the population that we actually collect data from.

In this case, the librarians are interested in the adult patrons of the library. Therefore, the population is all adult patrons of the library. The librarians examine the checkout records of $150$ randomly selected adult patrons. Therefore, the sample is the $150$ patrons selected.

3. Final Answer

The population is all adult patrons of the library; the sample is the 150 patrons selected.