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.
    Std normal distribution CDF plots.png

    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