The NORM.S.DIST function in Excel is a powerful tool used for statistical analysis. It provides the cumulative distribution for the standard normal distribution, which has a mean of zero and a standard deviation of one. This function is essential for various applications in probability and statistics, especially in hypothesis testing and confidence interval estimation.

Syntax

=NORM.S.DIST(z, cumulative)

• z: The z-score for which you want to calculate the distribution.
• cumulative: A logical value that determines the form of the function. If TRUE, NORM.S.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Example #1

=NORM.S.DIST(1.96, TRUE)

This function calculates the cumulative probability for a z-score of 1.96. The result is approximately 0.975, which indicates that about 97.5% of values lie below this z-score in a standard normal distribution.

Example #2

=NORM.S.DIST(0, TRUE)

This function computes the cumulative probability for a z-score of 0. The result is 0.5, indicating that 50% of values lie below this z-score, which is expected since 0 is the mean of the standard normal distribution.

Example #3

=NORM.S.DIST(-1, FALSE)

Here, the function returns the probability density for a z-score of -1. The result is approximately 0.24197, representing the height of the probability density function at that z-score.

Error handling

• VALUE!: This error occurs if the z parameter is not a number.
• NUM!: This error may appear if the cumulative parameter is not TRUE or FALSE.

Conclusion

The NORM.S.DIST function is an invaluable asset for anyone engaged in statistical analysis within Excel. By enabling users to easily calculate cumulative and density probabilities for standard normal distributions, it enhances decision-making and data understanding. Whether for academic, professional, or personal use, mastering this function can significantly improve your statistical toolset.