This is a very basic statistics question, which also leads in to a "how do I do it in JMP" question.

Imagine I have a component with a predicted defect rate of 0.5%. I build 500 systems which each use N of these components. The components are chosen at random and independently of each other. I can test for the defect at system level.

To my simple mind, if N=2 the probability of a system being good is 0.995^2 = 99.0025%, which means I should expect five systems out of 500 to fail test. If N=3, then this would change to 0.995^3*500 = 8 systems out of 500. This is just the binomial distribution.

Is this reasoning correct? If so, can I use JMP to calculate a confidence interval around this number, and is this even a meaningful question? What additional information do I need (e.g an estimate of the variation of the defect rate) for this?

Any suggestions or pointers to useful sections of the documentation would be much appreciated!

Many thanks!