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Norm inv

NORM.INV Function

The NORM.INV function in Excel is used to calculate the inverse of the normal cumulative distribution for a specified probability, mean, and standard deviation. In other words, it returns the value x such that the cumulative distribution function of the normal distribution equals a given probability.

Key Features of NORM.INV:

  • Converts a probability value from the cumulative normal distribution back into a corresponding x value.
  • Useful for statistical analysis, such as determining threshold values or z-scores for a specific probability level.

Syntax:

NORM.INV(probability, mean, standard_dev)
  • probability: Required. The cumulative probability for which you want to find the corresponding x value.
  • mean: Required. The mean (average) of the normal distribution.
  • standard_dev: Required. The standard deviation of the normal distribution.

How It Works:

The function computes the value of x using the inverse of the cumulative normal distribution function. For a given cumulative probability, it determines the corresponding data point in the normal distribution characterized by the specified mean and standard deviation.

Examples:

  1. Basic Example: To find the value of x such that the cumulative probability is 0.95 for a normal distribution with a mean of 50 and standard deviation of 10: 

    =NORM.INV(0.95, 50, 10)
    Result: 66.448.

  2. Real-Life Scenario: Assume test scores in an exam follow a normal distribution with a mean of 75 and a standard deviation of 15. To find the score corresponding to the top 5% of students (95th percentile): 

    =NORM.INV(0.95, 75, 15)
    Result: 99.674.

Notes:

  • Input Validation:

    • The probability parameter must be between 0 and 1. Otherwise, the function will return a #NUM! error.
    • If mean or standard_dev are non-numeric, the function returns a #VALUE! error.
    • A standard_dev value of 0 or negative will result in a #NUM! error.

  • Output Ranges:

    • The output value depends on the distribution parameters. For probabilities close to 0 or 1, the x value may approach extreme values.

Applications:

  • Statistical Analysis: Use NORM.INV to compute thresholds or determine cutoff points for specific percentiles within a dataset.
  • Finance: Estimate risk thresholds or calculate value-at-risk (VaR) in portfolio analysis.
  • Quality Control: Identify process limits for reaching a given defect probability.
  • Education: Determine exam score cutoffs corresponding to certain percentile ranks.

Tip: The NORM.INV function replaced the older NORMINV function starting with Excel 2010 to align with other statistical functions.

NOTE: The implementation is the same as NORMINV