continuous vs discrete
In the video pair over distributions, you referred to test scores as continuous. While they can be non-integer, they are not continuous. A test score is based on a ratio of correct questions to total questions. Since the number of total questions is finite, the scores are discrete. Even if the number of questions is prime and the ratio is a repeating decimal (e.g. 2 out of 3). The number of possible scores is still finite and discrete.
You referred to weights in another example. Weights are continuous.