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Manuals/calci/NORMALDISTRIBUTED (view source)
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<div style="font-size:30px">'''NORMALDISTRIBUTED(x,m,sd)'''</div><br/>
*<math>x</math> is the value for which distribution is evaluated.
*<math>m </math> is the mean.
*<math>sd</math> is the standard deviation.
==Description==
*This function gives the value of the normal probability distribution.
*It is the continuous probability distribution.
*The normal distributions are a very important class of statistical distributions.
*All normal distributions are symmetric and have bell-shaped density curves with a single peak.
*The term bell curve is used to describe the mathematical concept called normal distribution.
*It is also called as Gaussian distribution.
*The Normal Distribution has: mean = median = mode
*i.e., This distribution is symmetry about the center.
*Half of values less than the mean and half of values greater than the mean.
*In a normal distribution the probability values are satisfying the following conditions:
1. The total area under the curve is equal to 1 (100%)
2. About 68% of the area under the curve falls within 1 standard deviation.
3. About 95% of the area under the curve falls within 2 standard deviations.
4. About 99.7% of the area under the curve falls within 3 standard deviations.
*In a normal distribution the mean =0 and standard deviation =1,then the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate.
*It is the only absolutely continuous distribution.
*A normal distribution is calculated by :
<math>f(x,\mu,\sigma)=\frac {1}{\sigma\sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}</math>
where <math>\mu</math> is the mean and <math>\sigma</math> is the standard deviaton of the distribution.
==Examples==
#NORMALDISTRIBUTED(22,25,2.5) = -16.307435699813773,69.98317771544811,13.493570858283977,46.350299353375874 etc
#=NORMALDISTRIBUTED(30,36,20.9) = -39.85074927994863,24.24627001288364,23.575289380647483,-20.639707171803707,-8.8266089980268 etc.
==See Also==
*[[Manuals/calci/NORMDIST | NORMDIST ]]
*[[Manuals/calci/NORMSDIST | NORMSDIST ]]
*[[Manuals/calci/NORMINV | NORMINV ]]
==References==
*[http://stattrek.com/probability-distributions/normal.aspx Normal Distribution]