# Thread: Normal Distribution and symmetry

1. ## Normal Distribution and symmetry

Can you help me explain how to find probability using the idea that the normal distribution is symmetric? Thank you

2. ## Re: Normal Distribution and symmetry

For example, $\displaystyle P(-1 \le z \le 1) = 2P(0 \le z \le 1)$, using symmetry.

3. ## Re: Normal Distribution and symmetry

Thank you! If I have to explain this using words, how would I do that?

4. ## Re: Normal Distribution and symmetry

Hint: what does $\displaystyle P(-1 \le z \le 1)$ mean (in words)?

5. ## Re: Normal Distribution and symmetry

What about $\displaystyle P(Z>1) = P(Z<-1)$

How's this sound?

6. ## Re: Normal Distribution and symmetry

Clear as a bell

7. ## Re: Normal Distribution and symmetry

A random variable is said to have a normal distribution if it has a probability distribution that is symmetric and bell-shaped.

First, the total area under the curve is 1. The second is area will be used to measure probabilities. A normal distribution is intimately connected to Z-scores. The main idea is to standardize all the data that is given by using Z-scores. These Z-scores can then be used to find the area (and thus the probability) under the normal curve. Before getting into computing probabilities, here is a quick reminder of Z-scores.