Explain normal distribution and standardize it

## Statistics / Quant Risk Interview Question You are interviewing for a quant risk–leaning role. 1. **What are the key characteristics (properties) of a normal distribution** (Gaussian)? 2. Given a random variable \(X \sim \mathcal{N}(\mu, \sigma^2)\), **how do you standardize it** to obtain a standard normal random variable? Explain the transformation clearly. You may use equations and briefly mention common practical implications (e.g., probability mass within certain standard deviations).