# Standardizing the Normal Distribution

- Author:
- Gareth Daniels

- Topic:
- Normal Distribution

Two normal distributions in the form are shown.
The blue curve is and the black curve is with parameters controlled by the input boxes.
The shaded areas represent the probabilities shown, you can move the points to change the probabilities.

**Tasks**

- Set the black curve to
and find . - Find the value of
such that . - Set the black curve to
and find . - Find the value of
such that . - What do you notice?
- Set the black curve to
and find . - Find the value of
such that . - Set the black curve to
and find . - Find the value of
such that . - What do you notice?
- Test your findings by trying to find
if using the red area only, then check your answer.