Skip to content

Norm s inv

NORM.S.INV Function

The NORM.S.INV function in Excel is used to return the inverse of the standard normal cumulative distribution.
It finds the z-score corresponding to a given probability value under the standard normal distribution (mean of 0 and standard deviation of 1).

Key Features of NORM.S.INV:

  • Returns the z-score (number of standard deviations from the mean) for a given probability.
  • Useful in statistics, hypothesis testing, and probability analysis.

Syntax:

NORM.S.INV(probability)
  • probability: Required. A probability associated with the standard normal distribution. This value must be between 0 and 1 (exclusive).

How It Works:

The NORM.S.INV function is essentially the inverse of the cumulative probability function for the standard normal distribution.

For example:

  • A probability of 0.5 corresponds to a z-score of 0 (since the distribution is symmetric about the mean).
  • A smaller probability (e.g., 0.025) will correspond to a negative z-score (e.g., -1.96), indicating a value below the mean.
  • A larger probability (e.g., 0.975) will correspond to a positive z-score (e.g., 1.96), indicating a value above the mean.

Examples:

  1. Find the Z-Score for 95% Probability: To calculate the z-score for a probability of 0.95: 

    =NORM.S.INV(0.95)
    Result: 1.644854 (approximately).

  2. Central Probability: For a probability of 0.5 (the center of the standard normal distribution): 

    =NORM.S.INV(0.5)
    Result: 0 (mean of the standard normal distribution).

  3. Lower Tail: Calculate the z-score for the 2.5% lower tail probability: 

    =NORM.S.INV(0.025)
    Result: -1.959964 (approximately).

  4. Large Tail Probability: For a cumulative probability of 0.999: 

    =NORM.S.INV(0.999)
    Result: 3.090232 (approximately).

Notes:

  • Input Validation:

    • If probability is not between 0 and 1 (inclusive of boundaries), the function returns #NUM!.
    • If probability is non-numeric, the function returns #VALUE!.

  • Symmetry Property:

    • The function reflects the symmetry of the standard normal distribution. For example: 
      =NORM.S.INV(0.975) = 1.96, and =NORM.S.INV(0.025) = -1.96

Applications:

  • Confidence Interval Calculations: Use NORM.S.INV to find critical z-values for constructing confidence intervals in hypothesis testing.

  • Risk Assessment: Determine thresholds or cut-offs in predictive models based on probabilities.

  • Excel Charts with Normal Distribution: Use the z-scores returned by NORM.S.INV to mark specific points or percentiles on a visual representation of the standard normal distribution.

Tip: Combine NORM.S.INV with other distribution functions (e.g., NORM.DIST or NORM.INV) to work with non-standard normal distributions. Note: This is the same as NORMSINV