Example of a distribution plot with a shaded region

An engineer for a soda bottling facility collects data on soda can fill weights. The engineer determines that the fill weights follow a normal distribution with a mean of 12 ounces and a standard deviation of 0.25 ounces.

The engineer analyzes the distribution of the data to determine the probability that a randomly chosen can of soda has a fill weight that is between 11.5 and 12.5 ounces.

Note

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

  1. Open the Distribution Plot: Display Probability dialog box.
    • Mac: Statistics > Probability Distributions > Distribution Plot > Display Probability
    • PC: STATISTICS > Distribution Plot > Display Probability
  2. From Distribution, select Normal.
  3. In Mean, enter 12.
  4. In Standard deviation, enter 0.25.
  5. Under Shade the area corresponding to the following, select A specified x value.
  6. Click the Middle icon. This option shows the probability that is between two x-values.
  7. In X value 1, enter 11.5. In X value 2, enter 12.5.
  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 probability that a randomly chosen can of soda has a fill weight that is between 11.5 and 12.5 ounces is 0.9545.

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