The NORM.S.DIST function in Google Sheets is an essential tool for statistical analysis, specifically for working with the standard normal distribution. This function is useful for finding probabilities and cumulative distributions related to a standard normal variable, which has a mean of 0 and a standard deviation of 1.

Syntax

NORM.S.DIST(z, cumulative)

• z: This is the value for which you want to calculate the probability. It represents the number of standard deviations away from the mean.
• cumulative: This is a boolean value (TRUE or FALSE) that determines the form of the function. If TRUE, the function 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 of a standard normal variable being less than or equal to 1.96. The result is approximately 0.975, indicating that 97.5% of values lie below this z-score.

Example #2

NORM.S.DIST(-1.96, FALSE)

This function computes the probability density at z = -1.96. The result is about 0.058, representing the likelihood of observing a value exactly at -1.96 in a standard normal distribution.

Example #3

NORM.S.DIST(0, TRUE)

This calculates the cumulative probability of a standard normal variable being less than or equal to 0. The result is exactly 0.5, as 50% of values fall below the mean in a standard normal distribution.

Error handling

• NUM! This error occurs when the value of ‘z’ is non-numeric.
• VALUE! This error happens if ‘cumulative’ is not a boolean value (i.e., not TRUE or FALSE).
• N/A This may arise when either parameter is missing.

Conclusion

In summary, the NORM.S.DIST function in Google Sheets is a valuable asset for anyone engaged in statistical analyses involving the standard normal distribution. By understanding its syntax and how to handle errors, users can effectively utilize this function for calculating probabilities and making data-driven decisions.