Example of Cumulative Distribution Function (CDF)

The engineer at a bottling facility wants to determine the probability that a randomly chosen can of soda has a fill weight that is less than 11.5 ounces, greater than 12.5 ounces, or between 11.5 and 12.5 ounces. The engineer assumes that the fill weights of soda cans follow a normal distribution with a mean of 12 ounces and a standard deviation of 0.25 ounces.

Note

This example uses the normal distribution. However, these steps are similar for any distribution that you select.

  1. In an empty worksheet column, such as C1, type 11.5 and 12.5 into separate rows. These values are the fill weights for which the probabilities will be calculated.
  2. Open the Cumulative Distribution Function (CDF) dialog box.
    • Mac: Statistics > Probability Distributions > Cumulative Distribution Function
    • PC: STATISTICS > CDF/PDF > Cumulative Distribution Function
  3. From Form of input, select A column of values.
  4. From Values in, select C1.
  5. From Distribution, select Normal.
  6. In Mean, enter 12.
  7. In Standard deviation, enter 0.25.
  8. Under Output, select Display a table of cumulative probabilities. If you prefer to store the values in the worksheet, select Store cumulative probabilities in a column.
  9. Click OK.

Interpret the results

If the population of fill weights follows a normal distribution and has a mean of 12 and a standard deviation of 0.25, then the following are true:
  • The probability that a randomly chosen can of soda has a fill weight that is less than or equal to 11.5 ounces is the CDF at 11.5, which is approximately 0.023.
  • The probability that a randomly chosen can of soda has a fill weight that is greater than 12.5 ounces is 1 minus the CDF at 12.5, or 1 – 0.977250 = 0.02275.
  • The probability that a randomly chosen can of soda has a fill weight that is between 11.5 ounces and 12.5 ounces is the CDF at 12.5 minus the CDF at 11.5, or 0.977250 – 0.022750 = 0.954500.
Summary
Input
Mean
Standard deviation
Cumulative Probability
x
P(X ≤ x)
By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy