Statistical Trials

As I've mentioned over at TTD, I recently finished MPC1 (the first A Level module) and I enjoyed it greatly, though some things I have a less than complete handle on (any question that begins "Determine the condition on k" for example), and I fear my algebra isn't quite up to scratch. But I am struggling a bit with S1. I find it frustrating that the textbook does not try to provide proofs for several equations and that clear, detailed explanations are hard to come by. I also find reading values off distribution tables a pain. I simply don't have the feeling that I am understanding what is going on.

Here are my thoughts on the binomial distribution: this is a distribution of probabilities, when there are only two possible outcomes, which are independent, with a fixed number of trials and a fixed probability. Like tossing a coin x number of times. I can't think, off the top of my head, of lots of applications of this. Binomial distributions are determined by combinations of probabilities (ie if you are looking for the probability of finding x widgets that fails a test if 20% of widgets fail and you have a box of 200 widgets and you pick out 35, then it is 200C₃₅ because you could easily have loads of different ways of finding them, ie the first is ok, and the next isn't, etc etc). The 200C₃₅ would then be multiplied by the probabilities of success and failure, each raised to the power of x and 1-x.

Or something.

The normal distribution though is for continuous data and is based around a probability curve with the peak being the mean. But then you sort of turn it into a standard normal distribution with mean 0 to gauge the probabilities more easily. I'm not really sure of the logic of this to be honest. The normal distribution gives you probabilities of things like heights across a population. The curve is deviation from the mean - standard deviation, then, yes? Or not? So what is it we're really looking for on this curve?