I'm having trouble figuring out this question.

Suppose that we are interested in buying ball bearings from a certain manufacturer. We require very precisely manufactured ball bearings, and so we decide to investigate this manufacturer's output. In a random sample of 400 of the ball bearings, 48 of them contain manufacturing defects that make them useless to us.

What is a 95% confidence interval for the population proportion of defective balls?

a).12+0.0288

b).12+0.0298

c).12+0.0308

d).12+0.0318

e).12+0.0328

I'm using the equation: .12+1.96 * (stnd dev./ square root of n)

I estimated 2.4 as the standard deviation in the question before, but I think that might be wrong.

Also What is the 99% margin of error? I have no clue how to figure that out.

Some guidance on how to at least start this question/equation would be great.