# Normal Distribution and symmetry

• Jun 19th 2012, 03:37 PM
u12480
Normal Distribution and symmetry
Can you help me explain how to find probability using the idea that the normal distribution is symmetric? Thank you(Clapping)
• Jun 19th 2012, 03:39 PM
richard1234
Re: Normal Distribution and symmetry
For example, \$\displaystyle P(-1 \le z \le 1) = 2P(0 \le z \le 1)\$, using symmetry.
• Jun 19th 2012, 04:18 PM
u12480
Re: Normal Distribution and symmetry
Thank you! If I have to explain this using words, how would I do that?
• Jun 19th 2012, 05:54 PM
richard1234
Re: Normal Distribution and symmetry
Hint: what does \$\displaystyle P(-1 \le z \le 1)\$ mean (in words)?
• Jun 19th 2012, 06:56 PM
pickslides
Re: Normal Distribution and symmetry
What about \$\displaystyle P(Z>1) = P(Z<-1)\$

How's this sound?
• Jun 21st 2012, 05:34 AM
u12480
Re: Normal Distribution and symmetry
Clear as a bell
• Jun 22nd 2012, 12:04 PM
kalwin
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.