logistic regression with independent variable not-normally distributed (but potentially normally distributed) I have a question about logistic regression. I am trying to make a model to predict 0 or 1 from several continuous and categorical variables. I know that one continuous variable X  is normally distributed in the pool of participants, but I cannot get the dependent variable for all of them due to the cost. Therefore, I plan to perform a logistic regression with participants whose values of the variable X are high or low, that is, using only high group and low group, without the middle.
Note that, when getting the splitting pool of the variable X, other continuous variables keep normal distributions.
In this case that the variable X is known to be normally distributed in the participant pool, but the data used for prediction has such split distribution, is there any problem in logistic regression? Also, is there any problem when regularizing this logistic regression with elastic net?

You don't need any distribution for numerical predictors, neither in logistic regression nor in any other method, nor in regularization methods like GLMNet or similar. (A variable could be "number of children". That certainly won't be normally distributed, but it is perfectly fine as a predictor.)
Use all the data you can get, and if cost is a concern, sample over ranges where the model is important to you (what that means depends on your context).
