DocumentationFormulasFunctionsNorm s dist

NORM.S.DIST function

PRO

The NORM.S.DIST function in Jspreadsheet Formulas Pro returns the standard normal distribution, the normal distribution with mean 0 and standard deviation 1, for a given z-score. It is used to convert z-scores into probabilities in hypothesis tests and confidence intervals. With cumulative TRUE it returns the probability that a standard normal variable is less than or equal to z; with FALSE it returns the density at z. The compatibility function NORMSDIST returns only the cumulative form.

Documentation

Returns the standard normal distribution for a z-score.

Category

Statistical

Syntax

NORM.S.DIST(z, cumulative)

Parameter Description
z The z-score at which to evaluate the distribution.
cumulative TRUE returns the cumulative distribution function. FALSE returns the probability density function.

Behavior

The NORM.S.DIST function is equivalent to NORM.DIST(z, 0, 1, cumulative).

  • Both arguments are required. Calling the function with only z returns #N/A, so cumulative cannot be omitted as in Excel. Use NORMSDIST(z) for the one-argument cumulative form.
  • The cumulative probability is 0.5 at z equal to 0 and approaches 0 and 1 for large negative and positive z-scores.
  • The density at 0 is 0.398942, the peak of the standard normal curve.
  • Text arguments return #VALUE!.

Common Errors

Error Description
#VALUE! Returned when an argument is text that cannot be interpreted as a number.

Best practices

  • Always pass the cumulative argument, since the function does not accept the one-argument form.
  • When the input is a raw value rather than a z-score, compute (x - mean) / sd in a helper cell first so the formula stays readable.
  • Check with ISNUMBER that the z cell holds a number, because text returns #VALUE!.

Usage

A few examples using the NORM.S.DIST function.

NORM.S.DIST(-1.96, TRUE)
// Returns 0.024998

NORM.S.DIST(2, TRUE)
// Returns 0.97725

NORM.S.DIST(0, FALSE)
// Returns 0.398942, the density at zero

NORM.S.DIST(1.96)
// Returns #N/A because cumulative is required

Interactive Spreadsheet Demo

<html>
<script src="https://jsuites.net/v6/jsuites.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jspreadsheet@13/dist/index.min.js"></script>
<link rel="stylesheet" href="https://jsuites.net/v6/jsuites.css" type="text/css" />
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/jspreadsheet@13/dist/jspreadsheet.min.css" type="text/css" />

<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Material+Icons" />
<script src="https://cdn.jsdelivr.net/npm/@jspreadsheet/formula-pro/dist/index.min.js"></script>

<div id="spreadsheet"></div>

<script>
// You can use the following license for quick testing on localhost, StackBlitz, or CodeSandbox.
// The license is valid for one day, after which the spreadsheet will become read-only.
// For a longer trial period, you can create a free account and generate a demo license with an extended expiration date.
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

// Create a new spreadsheet
jspreadsheet(document.getElementById('spreadsheet'), {
  worksheets: [{
    data: [
    [
        "z",
        "cumulative",
        "NORM.S.DIST"
    ],
    [
        -1.96,
        true,
        "=NORM.S.DIST(A2, B2)"
    ],
    [
        0,
        true,
        "=NORM.S.DIST(A3, B3)"
    ],
    [
        1.96,
        true,
        "=NORM.S.DIST(A4, B4)"
    ],
    [
        0,
        false,
        "=NORM.S.DIST(A5, B5)"
    ]
]
  }]
});
</script>
</html>

import React, { useRef } from "react";
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/react";
import formula from "@jspreadsheet/formula-pro";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";

// Set license
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

export default function App() {
    // Spreadsheet array of worksheets
    const spreadsheet = useRef();

    // Worksheet data
    const data = [
    [
        "z",
        "cumulative",
        "NORM.S.DIST"
    ],
    [
        -1.96,
        true,
        "=NORM.S.DIST(A2, B2)"
    ],
    [
        0,
        true,
        "=NORM.S.DIST(A3, B3)"
    ],
    [
        1.96,
        true,
        "=NORM.S.DIST(A4, B4)"
    ],
    [
        0,
        false,
        "=NORM.S.DIST(A5, B5)"
    ]
];

    // Render component
    return (
        <Spreadsheet ref={spreadsheet}>
            <Worksheet data={data} />
        </Spreadsheet>
    );
}

<template>
    <Spreadsheet ref="spreadsheet">
        <Worksheet :data="data" />
    </Spreadsheet>
</template>

<script>
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/vue";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";
import formula from "@jspreadsheet/formula-pro";

// Set license
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

export default {
    components: {
        Spreadsheet,
        Worksheet,
    },
    data() {
        // Worksheet data
        const data = [
    [
        "z",
        "cumulative",
        "NORM.S.DIST"
    ],
    [
        -1.96,
        true,
        "=NORM.S.DIST(A2, B2)"
    ],
    [
        0,
        true,
        "=NORM.S.DIST(A3, B3)"
    ],
    [
        1.96,
        true,
        "=NORM.S.DIST(A4, B4)"
    ],
    [
        0,
        false,
        "=NORM.S.DIST(A5, B5)"
    ]
]

        return {
            data
        };
    }
}
</script>

import { Component, ViewChild, ElementRef } from "@angular/core";
import jspreadsheet from "jspreadsheet";
import formula from "@jspreadsheet/formula-pro";

// You can use the following license for quick testing on localhost, StackBlitz, or CodeSandbox.
// The license is valid for one day, after which the spreadsheet will become read-only.
// For a longer trial period, you can create a free account and generate a demo license with an extended expiration date.
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

@Component({
    standalone: true,
    selector: "app-root",
    template: `<div #spreadsheet></div>`
})
export class AppComponent {
    @ViewChild("spreadsheet") spreadsheet: ElementRef;
    // Worksheets
    worksheets: jspreadsheet.worksheetInstance[];

    // Create a new data grid
    ngAfterViewInit() {
        // Create spreadsheet
        this.worksheets = jspreadsheet(this.spreadsheet.nativeElement, {
            worksheets: [{
                data: [
    [
        "z",
        "cumulative",
        "NORM.S.DIST"
    ],
    [
        -1.96,
        true,
        "=NORM.S.DIST(A2, B2)"
    ],
    [
        0,
        true,
        "=NORM.S.DIST(A3, B3)"
    ],
    [
        1.96,
        true,
        "=NORM.S.DIST(A4, B4)"
    ],
    [
        0,
        false,
        "=NORM.S.DIST(A5, B5)"
    ]
]
            }]
        });
    }
}