(adsbygoogle = window.adsbygoogle || []).push({}); What exactly is "Density" and what am I calculating?

So I"m doing a lot of probability problems with CDF and although I know how to calculate it, I dont quite know what I am calculating (in terms of relating it to real life situations).

Example:

lets say the lifetime of a machine part has a continuous distribution of (0,40) with a density function that is proportional to (10x+2)^-2. What is the probability that the lifetime of a part is less than 5.

So I know how to solve this: integrate, find the density, and we get a value for C. Then, we integrate again to between 0 and 5 to get the probability that it is less then 5.

First of all, what is (0, 40) when they say there is a distribution between that? what does it mean that the probability of less than 5 is 5/12 (the correct answer)?

since 5 is on the lower end of (0, 40), is it saying that the part has a very low lifetime?

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# What exactly is Density and what am I calculating?

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