Manuals/calci/NORMALDISTRIBUTED

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 $\sigma$ is the standard deviaton of the distribution.

Examples

1. NORMALDISTRIBUTED(22,25,2.5) = -16.307435699813773,69.98317771544811,13.493570858283977,46.350299353375874 etc
2. =NORMALDISTRIBUTED(30,36,20.9) = -39.85074927994863,24.24627001288364,23.575289380647483,-20.639707171803707,-8.8266089980268 etc.

See Also

• NORMDIST
• NORMSDIST
• NORMINV

References

• Normal Distribution

• List of Main Z Functions

• Z3 home