Example of cumulative distribution function (CDF)

An engineer at a bottling facility wants to determine the probability that a randomly chosen bottle 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 bottle fill weights 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, you follow the same steps for any distribution that you select.

  1. In the column name cell of an empty worksheet column, type Weight.
  2. In separate rows, type 11.5 and 12.5. These values are the fill weights for which the probabilities will be calculated.
  3. Choose Calc > Probability Distributions > Normal.
  4. Select Cumulative probability.
  5. In Mean, enter 12.
  6. In Standard deviation, enter 0.25.
  7. In Input column, enter Weight.
  8. 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 bottle 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 bottle 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 bottle 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.

Cumulative Distribution Function

Normal with mean = 12 and standard deviation = 0.25 x P( X ≤ x ) 11.5 0.022750 12.5 0.977250
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