1. ## Confidence Interval problem.

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.

2. I would say

$\displaystyle p\pm Z\times \sqrt{\frac{p(1-p)}{n}} = 0.12\pm 1.96\times \sqrt{\frac{0.12(1-0.12)}{400}} = 0.12\pm 0.0318$