I'm solving this multiple choice question on the properties of a standardized variable. Two of the possible options (which are wrong but look right to me) are 1. It is always normally distributed and 2. it has a bell shaped distribution.
I've been googling and apparently, standardizing a variable does not change the shape of the curve. So if we have a non normal distribution- standardizing it wont change its shape. However, I thought one of the defining characteristic of a Z distribution was that it was symmetric.
If a normal distribution is always symmetric, and a Z distribution is always symmetric, how can we have a non normal standard distribution? Can we have a distribution that is not bell shaped and still standardized? I'm trying to think of examples but can't.