In reality, we have an infinite number of possible bell-shaped curves, and not only the standard curve.
Each probability distribution has its own expectation and standard deviation, and therefore its own bell-shaped curve. Our ability to calculate probabilities for standard normal distributions is of no use to us (for now) in calculating probabilities for other bell-shaped curves, while these account for most of the actual cases. But the mathematicians have come to our aid again.
They have found a way to turn any normal probability distribution (the target curve) into the standard normal probability distribution.
This method is called standardization. Standardization is actually a kind of translation of the values of any normal probability distribution into values corresponding to the standard bell-shaped curve (= the standardized values), which enables us to use the table.
It therefore follows that almost any problem we want to solve will include two separate operations:
Standardization.
Searching in the table.
The standardized values are called standard units.
The standardization operation represents the process of translating the target curve into the standard curve.
