The `NORM.S.DIST` function in Excel is used to calculate the standard normal cumulative distribution function. It is specifically designed for the standard normal distribution, which has a mean of 0 and a standard deviation of 1. Here’s how to use the function:
Syntax
NORM.S.DIST(z, cumulative)
- z: This is the value for which you want to calculate the distribution.
- cumulative: This is a logical value that determines the form of the function. If TRUE, the function returns the cumulative distribution function; if FALSE, it returns the probability density function.
Usage
- Cumulative Distribution: If you want to find the cumulative probability up to a certain z-value in a standard normal distribution, set the `cumulative` parameter to TRUE.
Example:
=NORM.S.DIST(1.5, TRUE)
This returns the cumulative probability that a standard normal random variable is less than or equal to 1.5.
- Probability Density: If you are interested in the height of the probability density function at a specific z-value, set the `cumulative` parameter to FALSE.
Example:
=NORM.S.DIST(1.5, FALSE)
This returns the density of the standard normal distribution at 1.5.
Example in Practice
Suppose you conduct a test and the z-score of one participant is 2.2. You want to know the probability that a participant achieves this score or less:
=NORM.S.DIST(2.2, TRUE)
This would give you the cumulative probability.
Similarly, if you want to know how common the exact z-score of 2.2 is, you would use:
=NORM.S.DIST(2.2, FALSE)
This would calculate the probability density at that exact point.
Points to Remember
- The `NORM.S.DIST` function is tailored for standard normal distributions. If your data is normally distributed but with a different mean or standard deviation, use the `NORM.DIST` function instead.
- Use the cumulative result to understand the percentile or rank of your z-score within a standard normal distribution.
- Use the probability density result for analyzing the likelihood of the specific z-score in terms of density.
This function is available in Excel 2010 and later versions.
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