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

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- Jun 19th 2012, 03:37 PMu12480Normal 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 PMrichard1234Re: 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 PMu12480Re: Normal Distribution and symmetry
Thank you! If I have to explain this using words, how would I do that?

- Jun 19th 2012, 05:54 PMrichard1234Re: Normal Distribution and symmetry
Hint: what does $\displaystyle P(-1 \le z \le 1)$ mean (in words)?

- Jun 19th 2012, 06:56 PMpickslidesRe: Normal Distribution and symmetry
What about $\displaystyle P(Z>1) = P(Z<-1)$

How's this sound? - Jun 21st 2012, 05:34 AMu12480Re: Normal Distribution and symmetry
Clear as a bell

- Jun 22nd 2012, 12:04 PMkalwinRe: 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.