If a random variable is normal, you can map it to a standard normal distribution (useful for finding probabilities in the standard normal table) by the following relationship:

**Example 1:** is normal. and Then

**Example 2:** has the same distribution as example 1. Then implies

Which implies:

Hence .

**With regard to Central Limit Theorem:**

By the *Central Limit Theorem*, the distribution of a sum of iid random variables converges to a normal distribution as the number of iid random variables increases. This means that if the number of iid random variables is sufficiently large, we can get approximate probabilities by using a normal distribution approximation.