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Documentation/Calc Functions/NORMSDIST

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Function name:

NORMSDIST

Category:

Statistical Analysis

Summary:

Calculates values from the cumulative distribution function of the standard normal distribution.

The normal distribution is also known as the Gaussian distribution. It is a family of continuous probability distributions used in many fields to represent independent, randomly generated variables. The standard normal distribution is the normal distribution that has a mean of 0 and a standard deviation of 1.

Syntax:

NORMSDIST(Number)

Returns:

Returns a real number in the range [0, 1], which is the value of the cumulative distribution function from the standard normal distribution for the given argument.

Arguments:

Number is a real number, or a reference to a cell containing that number, which is the value at which the cumulative distribution function of the standard normal distribution is to be evaluated.

  • If Number is non-numeric, then NORMSDIST reports a #VALUE! error.

Additional details:

  • Calc provides three related functions for calculating values from the standard normal distribution:
  • NORM.S.DIST. Calculates a value from either the probability density function or the cumulative distribution function, depending on the setting of the Cumulative argument. Provided for interoperability with Microsoft Excel.
  • NORMSDIST. Calculates a value from the cumulative distribution function, in accordance with the LEGACY.NORMSDIST function of ODF 1.2.
  • PHI. Calculates a value from the probability density function, in accordance with the PHI function of ODF 1.2.
  • For the standard normal distribution, the following relationships exist between relevant Calc functions:
[math]\displaystyle{ \text{NORM.DIST}(x;\:0;\:1;\:c)\:=\:\text{NORM.S.DIST}(x;\:c)\:=\:\text{NORMSDIST}(x) }[/math]
  • The formula for the cumulative distribution function of the standard normal distribution is:
[math]\displaystyle{ CDF_{std\_normal}(x)~=~\int_{-\infty }^{x}\frac{1}{\sqrt{2\pi}}~\text{EXP} \left(-\frac{1}{2}\ t^2 \right) \:dt }[/math]
  • The following figure shows the cumulative distribution function for the standard normal distribution.

Examples:

Formula Description Returns
=NORMSDIST(A1) where cell A1 contains the number 0. Here the function calculates the cumulative distribution function of the standard normal distribution for the value 0. 0.5
=NORMSDIST(1) Here the function calculates the cumulative distribution function of the standard normal distribution for the value 1. Hence, 84% of the area under the curve of the standard normal distribution lies to the left of the value 1. 0.841344746068543

Related LibreOffice functions:

NORM.DIST

NORM.INV

NORM.S.DIST

NORM.S.INV

NORMDIST

NORMINV

NORMSINV

PHI

ODF standard:

Section 6.18.54, part 2

Related (or similar) Excel functions:

NORMSDIST