Confidence Intervals

[babypurin]

I need help with this homework problem:

"An investment analyst constructed the following 99% confidence in-
terval for the probability of default of a B-rated bond based on a random
sample of B-rated bonds:

(0.0107, 0.1143).

4.1 What is the proportion of bonds in her sample that defaulted?

4.2. A bond rating agency claims that 5% of all B-rated bonds will
default. What can you conclude about this claim based on the confidence
interval in 4.1.?

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I know how to solve for the confidence interval, but I don't know how to work backwards, especially since we are given no information about the sample size and/or standard deviation. It seems that we would would want to be solving for x bar in this equation, but I don't know how to do it given the paucity of information in the question.

[Rounds]

I was going to say ask yourself simpler questions to start with but my example of one is the first question.

4.1 is really testing whether you can relate to the idea of a symmetric confidence interval. What's at its center?

Then the next question is whats a sample proportion defined as? (Dont answer that before answering 4.1)

Then ponder some plugging and chugging in these:
http://davidmlane.com/hyperstat/B9168.html