When constructing a CI for population correlation coefficient (p), I am told you cannot use +/- 1.96 as the sampling distribution is non-normal? However, I am also told that each X and Y are assumed to be pairs of independent observations from a bivariate normal distribution?

How come normality is an assumption but it cannot be used to calculate CI?

Many thanks for your time. I hope this question makes sense!

Kind regards,

SF