# Normally distributed estimated parameters in logistic regression

I was reading the book Introduction to Statistical learning, where in z statistic was used to for hypothesis testing for parameters, so my doubt is that as response variable is not normally distributed here (at all) so parameters basically get their distribution from the response variable assumption of normality, right? so how come Z statistic exists,for parameter that is not normal?

Well, you can define the $Z$ statistic by the same formulas (well, actually using asymptotic approximations) that is used in the normal case. There is no implication that the resulting statistic do have a normal distribution. It might have so, but only as an asymptotic approximation.