Manuals/calci/NORMAL

NORMALDISTRIBUTED(x,m,sd)

• $x$ is the value for which distribution is evaluated.
• $m$ is the mean.
• $sd$ 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

$f(x,\mu ,\sigma )={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{\frac {-(x-\mu )^{2}}{2\sigma ^{2}}}$, where $\mu$ is the mean and <math>\sigma<\math> is the standard deviaton of the distribution.

where , and

RANDOMNUMBERGENERATION(Number, RandomNumber, Distribution, NewTableFlag, Mean, StandardDeviation)

where,

Number - represents the number of variables.

RandomNumber - represents the number of random number.

Distribution - represents the distribution method(i.e normal) to create random values.

NewTableFlag - is the TRUE or FALSE.If set as TRUE,the result in new sheet. If NewTableFlag is omitted, it assumed to be FALSE.

Mean - represents the Mean.

StandardDeviation - represents the standard deviation.

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Normal Distribution characterized by a mean and a standard deviation.

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Lets see an example in (Column3Row1)

?UNIQeebbe8a3183fa626-nowiki-00000004-QINU?

RANDOMNUMBERGENERATION returns the result in new sheet(5Space).

?UNIQeebbe8a3183fa626-nowiki-00000005-QINU?

RANDOMNUMBERGENERATION returns the #ERROR(Number < 0).

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RANDOM NUMBER GENERATION : NORMAL

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Syntax

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Remarks

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Examples

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Description

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If Number < 0 or RandomNumber < 0, RANDOMNUMBERGENERATION returns the #ERROR.

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	Column1	Column2	Column3	Column4
Row1	5Space
Row2	File:Copy-cube.gif
Row3
Row4
Row5
Row6

File:Calci1.gif

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Random Number Generation
Normal Distribution

-0.6469271541994427	-1.9074080903736057	-0.617997136104105
-0.7646726307858795	-0.12686814329075044	-1.0016839542241755
1.5847698409152808	0.6334613031585946	-0.4798269568260549
-1.6687086155351085	1.102906962994111	1.4347768240383833

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