Difference between revisions of "Manuals/calci/NORMDIST"
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*In <math> NORMDIST(x,m,sd,cu) ,x</math> is the value of the function,<math> m</math> is the arithmetic mean of the distribution, <math>sd</math> is the standard deviation of the distribution and <math>cu</math> is the logical value that indicating the form of the function. | *In <math> NORMDIST(x,m,sd,cu) ,x</math> is the value of the function,<math> m</math> is the arithmetic mean of the distribution, <math>sd</math> is the standard deviation of the distribution and <math>cu</math> is the logical value that indicating the form of the function. | ||
*Suppose cu is TRUE, this function gives the cumulative distribution, and it is FALSE, this function gives the probability mass function. | *Suppose cu is TRUE, this function gives the cumulative distribution, and it is FALSE, this function gives the probability mass function. | ||
| − | *The equation for the normal distribution is: <math> f(x,\mu,\sigma)=\frac{1}{\sigma \sqrt{2\pi}}.e^{-\left({\ | + | *The equation for the normal distribution is: <math> f(x,\mu,\sigma)=\frac{1}{\sigma \sqrt{2\pi}}.e^{-\left({\tfrac{(x-\mu)^2}{2\sigma^2}}\right)}</math> where <math>\mu</math> is the mean of the distribution,<math>\sigma</math> is the standard deviation of the distribution. |
*In this formula, Suppose <math>\mu</math> = 0 and <math>\sigma</math>= 1, then the distribution is called the standard normal distribution or the unit normal distribution. | *In this formula, Suppose <math>\mu</math> = 0 and <math>\sigma</math>= 1, then the distribution is called the standard normal distribution or the unit normal distribution. | ||
This function will return the result as error when any one of the argument is non-numeric and <math>sd<=0</math>. | This function will return the result as error when any one of the argument is non-numeric and <math>sd<=0</math>. | ||
Revision as of 23:06, 7 January 2014
NORMDIST(x,m,sd,cu)
- 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 x} is the value,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 m} is the mean,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 sd} is the standard deviation and 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 cu} is the logical value like TRUE or FALSE.
Description
- This function gives the normal distribution for the particular mean and standard deviation.
- Normal distribution is the function that represents the distribution of many random variables as a symmetrical bell-shaped graph.
- This distribution is the continuous probability distribution.It is also called Gaussian distribution.
- In 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 NORMDIST(x,m,sd,cu) ,x} is the value of the function,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 m} is the arithmetic mean of the distribution, 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 sd} is the standard deviation of the distribution and 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 cu} is the logical value that indicating the form of the function.
- Suppose cu is TRUE, this function gives the cumulative distribution, and it is FALSE, this function gives the probability mass function.
- The equation for the normal distribution is: 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^{-\left({\tfrac{(x-\mu)^2}{2\sigma^2}}\right)}} where is the mean of the distribution,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 \sigma} is the standard deviation of the distribution.
- In this formula, Suppose 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 \mu} = 0 and 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 \sigma} = 1, then the distribution is called the standard normal distribution or the unit normal distribution.
is the mean of the distribution,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 \sigma}
is the standard deviation of the distribution. This function will return the result as error when any one of the argument is non-numeric and 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 sd<=0}
.
- when 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 cu} is TRUE , this formula is the integral from 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 -\infty} to 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 x} and 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 cu} is FALSE , we can use the same formula.
Examples
- =NORMDIST(37,29,2.1,FALSE) = 0.000134075
- =NORMDIST(37,29,2.1,TRUE) = 0.99993041384
- =NORMDIST(10.75,17.4,3.2,TRUE) = 0.01884908749
- =NORMDIST(10.75,17.4,3.2,FALSE) = 0.014387563