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Norm dist

NORMDIST Function

The NORMDIST function in Excel is used to calculate the normal distribution for a given value.
The normal distribution is a bell-shaped curve used to represent data that is evenly distributed around a mean.

Key Features of NORMDIST:

  • Computes the probability density or cumulative probability of a value based on the normal distribution.
  • Useful for statistical analysis, such as evaluating probabilities, z-scores, or distributions in data.

Syntax:

NORMDIST(x, mean, standard_dev, cumulative)
  • x: Required. The value for which you want to calculate the distribution.
  • mean: Required. The mean (average) of the distribution.
  • standard_dev: Required. The standard deviation of the distribution.
  • cumulative: Required. A logical value that determines the type of distribution to be calculated:
    • TRUE: Returns the cumulative distribution function (CDF), the probability that x is less than or equal to a value.
    • FALSE: Returns the probability density function (PDF), the height of the distribution curve at x.

How It Works:

The NORMDIST function uses the formulas for either the cumulative or probability density function of the normal distribution:

  1. Probability Density Function (PDF): For cumulative = FALSE, the formula used is: 

    PDF = (1 / (standard_dev * SQRT(2 * PI))) * EXP(-(x - mean)^2 / (2 * standard_dev^2))
    This computes the height of the normal distribution at x.

  2. Cumulative Distribution Function (CDF): For cumulative = TRUE, the function uses integration to calculate the area under the curve to the left of x.

Examples:

  1. Basic Example (PDF): To calculate the probability density for x = 50, with a mean of 45 and standard deviation of 10: 

    =NORMDIST(50, 45, 10, FALSE)
    Result: 0.0352065.

  2. Cumulative Distribution Example (CDF): To find the cumulative probability that a value is less than or equal to 70, where the distribution has a mean of 65 and a standard deviation of 15: 

    =NORMDIST(70, 65, 15, TRUE)
    Result: 0.630558.

  3. Real-Life Scenario: A company tracks its employees' test scores, which follow a normal distribution with a mean of 80 and a standard deviation of 10. To determine the probability of a score below 90: 

    =NORMDIST(90, 80, 10, TRUE)
    Result: 0.841345.

Notes:

  • Input Validation:

    • If standard_dev is 0 or negative, the function returns #NUM!.
    • If any input is non-numeric, the function returns #VALUE!.

  • Choosing Between PDF and CDF:

    • Use FALSE for probability density when you are interested in the height of the curve at a specific point.
    • Use TRUE for cumulative probability when you need the total probability up to a point.

  • Output Ranges:

    • The cumulative probability (cumulative = TRUE) output value is always between 0 and 1.
    • The probability density (cumulative = FALSE) is not bounded between 0 and 1.

Applications:

  • Statistical Analysis: Evaluate normal probabilities for statistical tasks like hypothesis testing or data modeling.
  • Finance: Calculate probabilities for returns, prices, or risk analysis.
  • Quality Control: Check how a measurement compares to a process's mean.
  • Healthcare: Model probabilities of data based on patient statistics.

Tip: The NORMDIST function was replaced by the NORM.DIST function in Excel 2010 and later versions, which supports similar functionality with enhanced features.