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Math Help - Normal Distribution and symmetry

  1. #1
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    Normal Distribution and symmetry

    Can you help me explain how to find probability using the idea that the normal distribution is symmetric? Thank you
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  2. #2
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    Re: Normal Distribution and symmetry

    For example, P(-1 \le z \le 1) = 2P(0 \le z \le 1), using symmetry.
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  3. #3
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    Re: Normal Distribution and symmetry

    Thank you! If I have to explain this using words, how would I do that?
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  4. #4
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    Re: Normal Distribution and symmetry

    Hint: what does P(-1 \le z \le 1) mean (in words)?
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  5. #5
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    Re: Normal Distribution and symmetry

    What about P(Z>1) = P(Z<-1)

    How's this sound?
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  6. #6
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    Re: Normal Distribution and symmetry

    Clear as a bell
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  7. #7
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    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.
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