Excel offers you the NORM.DIST statistical function for working with normal distributions. The NORM.DIST function calculates the probability that variable X falls below or at a specified value. The NORM.DIST function uses the syntax
=NORM.DIST(x,mean,standard_dev,cumulative)
where x is the variable that you want to compare, mean is the population mean, standard_dev is the population standard deviation, and cumulative is a logical value that tells Excel whether you want a cumulative probability or a discrete probability.
Here's an example of how you might use the NORM.DIST function: Suppose you want to calculate the probability that some goofball with whom you work actually does have an IQ above 135 like he’s always bragging. Further suppose that the population mean IQ equals 100 and that the population standard deviation for IQs is 15.
In this case, you use the following formula:
=NORM.DIST(135,100,15,1)
The function returns the value .990185, indicating that if the inputs are correct, roughly 99 percent of the population has an IQ at or below 135. Or, slightly restated, this means the chance that your co-worker has an IQ above 135 is less than 1 percent.
If you want to calculate the probability that your co-worker has an IQ equal to exactly 135, use the following formula:
=NORM.DIST(135,100,15,0)
This function returns the value .001748 indicating that .1748 percent, or roughly one-sixth of a percent, of the population has an IQ equal to 135.
To be very picky, statisticians might very well tell you that you can’t actually calculate the probability of a single value, such as the probability that somebody’s IQ equals 135. When you set the cumulative argument to 0, therefore, what actually happens is that Excel roughly estimates the probability by using a small range about the single value.
