Final answer:
The transformed random variable Z = (X - μ) / σ has a mean of 0 and a standard deviation of 1, resulting in a standard normal distribution known as z-score.
Step-by-step explanation:
If the random variable X has a mean of μ (mu) and a standard deviation of σ (sigma), then the transformed random variable Z = (X - μ) / σ has a mean and standard deviation, respectively. Applying the transformation to X standardizes it, resulting in a standard normal distribution with a mean of 0 and a standard deviation of 1. This is because any number subtracted by itself is 0 (which is what happens to the mean in the numerator), and any number divided by itself is 1 (which is the case for the standard deviation in the denominator). The transformation is commonly referred to as calculating the z-score, which allows us to compare data from different normal distributions.