A confidence interval is considering one estimated range that is showing values of unknown population mater than after that, estimated range will be calculated. One of the most important things in confidence interval are independent samples which copies are going to be taken repeatedly from the one same population. Confidence interval will do calculation of those samples and then after that there is coming a percentage of intervals.
The larger population a state had, the more representation they got in Congress so southern states did want slaves to count towards the states population. Thus, slaves would ultimately be counted and 3 out of every 5 slaves were counted as people.