Why z-score is used instead of a t-score for confidence Interval of proportion parameter

statistics

#1

I am currently studying about confidence Interval of any parameter of a population like mean and proportion while studying I came across a two formula one for mean and other for proportion.

formula for proportion

formula for mean.

I want to know why we have used the z-statistics in place of t-statistics when calculating a confidence interval for a proportion .


#2

T-statistics is used for unknown Variance / sample size is <30

z- Statistics for known Variance / sample size is >30 .

Because the approximation of normal Distribution can be done if sample size > 30 as per the empirical rule

please correct me if i am wrong