Manuals/calci/NORMAL

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NORMALDISTRIBUTED(x,m,sd)


  • is the value for which distribution is evaluated.
  • is the mean.
  • 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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x,\mu,\sigma)=\frac {1}{\sigma\sqrt(2\pi) e^{\frac{-(x-\mu)^2}{2\sigma^2}} , where 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.


Normal Distribution characterized by a mean and a standard deviation.

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).


RANDOM NUMBER GENERATION : NORMAL


Syntax

Remarks

Examples

Description

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


Column1 Column2 Column3 Column4
Row1 5Space
Row2
Row3
Row4
Row5
Row6

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