A correction factor for the z value can be implented when the population under study is large, negative, small or inverted?

A continuity correction factor is used when you use a continuous function to approximate a discrete one. For example, when you want to approximate a binomial with a normal distribution. According to the Central Limit Theorem, the sample mean of a distribution becomes approximately normal if the sample size is large enough. The binomial distribution can be approximated with a normal distribution too, as long as n*p and n*q are both at least 5. So the answer is large