>Having an understanding of what a derivative or integral of a function is a good insight to have, no doubt.
Learning calculus is to statistics what getting undressed is to sex.
1] You have to learn algebra so that you can figure out how to take derivatives.
2] You have to learn derivatives to learn how to integrate.
3] Once you can integrate you can integrate y=1/x from 1 to x and then learn what a logarithm is (real, Naperian logarithms, not log10 that the engineers uze.)
4] Then you can evaluate the integral of y=1/x from 1 to infinity and discover from where arises 'e' the base of logarithms.
5] *NOW* you can contemplate e to the negative x squared and understand the distribution of men's chest sizes and distributions normal and otherwise.
To claim you know anything about statistics with out knowing integral calculus is to make the silly claim that you know all about sex from having seen a few copies of Playboy. To understand sex you and a partner must get out of you clothes, and once you get good at it you will need a shower afterwards. To understand statistics is just as much work, just as messy and just as rewarding; and just like sex, not something one brings up in every social circumstance.