The Probability Density Function (PDF) is referred to as the shape of the distribution.

As a histogram of the distribution is created with more and more categories it begins to take on the exact shape of the distribution.

If you were to draw a curved line that fits most of the histogram (created from the samples) it would create a model that describes the population.

*X-axis: represents the z-scores of measurement*

*Y-axis: represents, within +/- 0.5 standard deviation, the probability of "x" occurring with each "x" being independent*

We will call f(x) the PDF which is the curved line overlaid on the samples of the histogram. The area to the left of x (point of interest) is equal to probability of the x-axis variable being less than the value of x (point of interest). The probability density is the y-axis.

The PDF works for discrete and continuous data distributions. There PDF must be positive for all values of x since there can not be a negative value for probability.

The PDF represents the entire amount of space under the curve and the highest probability that exist is 100% or 1.00 the entire area under the curve = 1.

So, from negative infinity to positive infinity, the area under the curved line is represented by the following:

The PDF for discrete data for all values of *k* with f(x) greater than or equal to 0:

The integral of the PDF to the left of a point of interest, x, is the Cumulative Distribution Function.

The function NORM.DIST (former Excel version used NORMDIST) calculates the Normal Probability Density Function __or__ the Cumulative Normal Distribution Function.

With "x" as the point of interest, the format of the function is:

*NORMDIST(x, mean, standard deviation, TRUE or FALSE)*

In the final argument use TRUE for the Cumulative Normal Distribution Function and use FALSE for the Normal Probability Density Function.

Custom Search

**Six Sigma**

**Templates, Tables & Calculators**

**Six Sigma Certification**

**Six Sigma** Modules

*Green Belt Program (1,000+ Slides)*

*Basic Statistics*

*SPC*

*Process Mapping*

*Capability Studies*

*MSA*

*Cause & Effect Matrix*

*FMEA*

*Multivariate Analysis*

*Central Limit Theorem*

*Confidence Intervals*

*Hypothesis Testing*

*T Tests*

*1-Way Anova Test*

*Chi-Square Test*

*Correlation and Regression*

*Control Plan*

*Kaizen*

*Error Proofing*