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Math Help - What is a Normal Distribution and how does Standard Deviations work?

  1. #1
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    What is a Normal Distribution and how does Standard Deviations work?

    Can anybody explain to me what characteristics make a distribution a normal distribution?

    The only one I am sure about is that a Normal Distribution is symmetrical.

    -What about the 68,95,99.7 rule in which 68% of the distribution fall under the first standard deviation, 95% fall into the second, and 99.7% fall into the third? Is this a necessary property of a Normal Distribution?

    Finally, this is what I am primarily uncertain about. Some distributions show signs of kurtosis in which a lot of values end up around the mean or are at the tail. Are these distributions also Normal Distributions? And does the 68, 95, 99.7 rule apply to these distributions also. In other words, if a distribution is highly peaked in which many of the values fall around the mean, does the first standard deviation still encompass 68% of the distribution?
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  2. #2
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    Re: What is a Normal Distribution and how does Standard Deviations work?

    a random variable has a normal distribution if and only if it has the normal probability density function.

    All normally distributed variables have the standard deviation rule you mentioned.

    The normal distribution has excess kurtosis of 0. Any distribution with any other amount of excess kurtosis is not a normal distribution, and wont have the properties of the normal distribution except by coincidence.

    Kurtosis - Wikipedia, the free encyclopedia
    Last edited by SpringFan25; October 2nd 2011 at 02:52 PM.
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