I've had great success with some of the replies before and I am looking to get my head around this figure which popped up.

I am ok with the general idea around Confidence limits but I got stuck when asked this question that deals with finding confidence levels of probabilities for example I was asked;

Please state the 95% Confidence Limits as a whole number percentage, for the proportion of cars that are Black.

There are 43 Black cars out of 144 all together.

For 95% confidence Z=1.9600 p=43/144=0.29861 So in percentage terms lower limit = (0.29861 -1.96x0.038137)*100 upper limit = (0.29861 +1.96x0.038137)*100

What I was finding difficult was locating the number 0.038137?

Where would this number come from? I am happy about finding the percentage then taking away the 95% confidence level of 1.96 to find the lower limit but what are they multiplying it by?