Normal Probability Distribution

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Normal Probability Distribution

The normal, or Gaussian, probability distribution has a bell-shaped curve. It is characterized by its mean mu and standard deviation sigma. The mean describes the location of the curve, the standard deviation describes the shape (how peaked or flat it is). The mean, the median, and the mode are all equal in a normal distribution.

NORMDIST

If you have a normal distribution and know the mean and standard deviation, you can find the probability that a random variable x falls below a given value using the NORMDIST function. The NORMDIST uses the following syntax

=NORMDIST(x, mean, standard deviation, cumulative)

For example, if containers are filled with an average of 591 ml of liquid, and the volumes are normally distributed around this mean with a standard deviation of 3 ml, you can find the probability that a container has less than 586 ml of liquid. To do this, enter 586 for the first parameter x, 591 for the second parameter, 3 for the third parameter, and TRUE for the fourth parameter. The function looks like this:

=NORMDIST (586,591,3,TRUE)

The function returns the value 0.0477. So there’s about a 4.8% chance that a container holds less than 586 ml. You can find the probability that a value falls between a certain range by making a few simple calculations, remembering that there’s a 0.5 probability that a value falls on each side of the mean. For example, if you want to find the probability that a container holds between 585 and 593 ml of liquid, you find the probability that it contains less than 585 and subtract this from 0.5. Then you find the probability that it contains less than 593 and subtract 0.5. Then you add these two figures.

Tip: Because a normal distribution is a continuous distribution, probabilities are areas under the probability density function and the probability of any single value for the random variable is zero. However, if you set the Cumulative parameter to FALSE, you can approximate the probability of a discrete value by setting a small range around that value.

NORMINV

If instead of having a value and needing to find the probability that a random variable falls below it, you know the probability for the range into which a random variable must fall and need to find the value defining this range, you can use the NORMINV function.

The NORMINV function uses the following syntax:

=NORMINV (probability, mean, standard deviation)

Using the previous example for the NORMDIST function, if the mean fill volume in a set of containers is 591ml with a standard deviation of 3ml, and you want to be able to say that there’s a 99% probability of a container holding more than a certain volume of fluid (i.e., you want to find an amount below which the area under the curve is 0.01), enter the function as follows:

=NORMINV (0.01,591,3)

The function returns the value 584.02, meaning that there’s a 1% probability of a container filled with less than this amount.

Article Source: http://articlenexus.com

Prolific computer book author Stephen L. Nelson wrote the MBA's Guide to Microsoft Excel, from which this short article is adapted. Nelson also writes and edits downloadable do-it-yourself small business incorporation kits that businesses and investors can use for setting up a Tennessee S Corporation , Washington S Corporation .

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