(I have asked this question in the math site, but think it might be more relevant here) I have been following the online MIT statistics course, and one course was about some fundamental distributions.(https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading5c.pdf)
I read it a couple of times and did a lot of search online, but I still find it hard to fully grasp the idea of how to match different distributions to different real life scenarios.
For example, "Suppose we have a tape measure with markings at each millimeter. If we measure (to the nearest marking) the length of items that are roughly a meter long, the rounding error will uniformly distributed between -0.5 and 0.5 millimeters." I just cannot wrap my head around how it was determined that uniform distribution matches this case.
I'm wondering if there are some books/articles that give detailed and intuitive explanation of distributions and their real life applications?