The main formula we'll be using is e = zσ/√n. Since we're dealing with a margin of error as a percentage, we can use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. That takes care of σ, which is 1. We also know that margin of error e is 0.04. Now we need the z value for a 95% confidence level. We might be given this, but if not, then we can think of this margin of error as the upper and lower boundaries of an area that is 0.95 in the standard normal graph and is symmetrical around the mean of 0. This would make the right half have an area of 0.475. This means that the cumulative area to the left of the far right marker is this 0.475 plus the 0.5 that is the entire left half of the normal curve. So we need the z value that gives us a cumulative area of 0.975. This z value is 1.96.
We can now plug them into the equation: 0.04 = 1.96/√n
Do a little algebra to isolate n:
0.04√n = 1.96
√n = 1.96/0.04
√n = 49
n = 2401
If you have software or a calculator that can do confidence intervals, you can always test this to see if this sample size and this confidence level gets you. 0.04 margin of error on a standard normal curve. I would highly recommend this as a last step to get the concept more solid in your mind.
