Cumulative Distribution Function

The Cumulative Distribution Function (CDF) of a continuous random variable, x, is equal to the integral of its probability density function (PDF) to the left of x. This value represents the area below the PDF to the left of the point of interest, x.

Cumulative Density Function

X-axis: represents z-scores of measurement

Y-axis: represents the probability (cdf) of "x" or lower occurring. The range is 0-1 with 1 representing 100% of the values of "x". 

A y-value of 0.5 is at the mean "x" value.

The CDF is a graphical display of the total % of results below a specific measurement. Histograms and PDF show the probabilities over a range of values.


If the PDF of a continuous random variable is known to be 0.08x where x is valid from 0 to 5. Find the probability (cumulative distribution function) of x being less or equal to 2.3. 

Normal CDF in Excel

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, or
  • FALSE for the Normal Probability Density Function.

CDF calculation in Excel

An example is shown below For the CDF given:

x = 12.65

Mean = 12.5

Standard Deviation = 0.25

The CDF = 72.6%

CDF in Excel

Inverse CDF

The inverse cumulative distribution function is used to estimate "x" where a certain percent of probability has occurred.

Finding Probability Distributions in Minitab

You can find the PDF, CDF, and Inverse CDF for several types of distributions. Shown below is a snapshot of the menus. 


Return to the MEASURE Phase

Go to the Probability Density Function (PDF)

Templates and Calculators

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