In Carcelle-le-Grignon at the end of the eighteenth century, there were 2009 births. There were 983 boys and 1026 girls. You can regard this as a fair random sample (with replacement, though try not to think too hard about what that means) of births. If you map each female birth to 1 and each male birth to 0, the probability of a female birth is the population mean of this random variable. You have a sample of 2009 births. (a) Using the reasoning and data above, construct a 99% confidence interval for the probability of a female birth.

(b) Using the reasoning and data above, construct a 99% confidence interval for the probability of a male birth.

(c) Do these intervals overlap? what does this suggest?

I especially wonder the mapping part. What does that contribute to the answer?