2 In order to estimate the total number of rabbits in a certain region, a random sample of 500 rabbits is captured, marked and released. After two days a random sample of 250 rabbits is captured and 24 are found to be marked. It may be assumed that there is no change in the population during the two days.
- Estimate the total number of rabbits in the region.
- Calculate an approximate \(95 \%\) confidence interval for the population proportion of marked rabbits.
- Using your answer to part (ii), estimate a 95\% confidence interval for the total number of rabbits in the region.